distributed time varying quadratic optimization for multiple agents under undirected graphs this paper considers a class of distributed quadratic optimization problem under an undirected and connected graph different from most of the existing distributed optimization works that consider the optimal solutions to be constants the optimal solution and the objective functions at the optimal solution are both assumed to be time varying for the case where there is no constraint on the decision variables gradient based searching methods are proposed to track the unknown optimal solution the tracking errors are proven to be asymptotically stable for the case where there exists a local compact convex constraint set for each agent projected gradient based methods are proposed for both neighboring coupled and generally coupled objective functions and the tracking errors are proven to be uniformly ultimately bounded with arbitrarily small bound

approximate primal solutions and rate analysis for dual subgradient methods in this paper we study methods for generating approximate primal solutions as a byproduct of subgradient methods applied to the lagrangian dual of a primal convex possibly nondifferentiable constrained optimization problem our work is motivated by constrained primal problems with a favorable dual problem structure that leads to efficient implementation of dual subgradient methods such as the recent resource allocation problems in large scale networks for such problems we propose and analyze dual subgradient methods that use averaging schemes to generate approximate primal optimal solutions these algorithms use a constant stepsize in view of its simplicity and practical significance we provide estimates on the primal infeasibility and primal suboptimality of the generated approximate primal solutions these estimates are given per iteration thus providing a basis for analyzing the trade offs between the desired level of error and the selection of the stepsize value our analysis relies on the slater condition and the inherited boundedness properties of the dual problem under this condition it also relies on the boundedness of subgradients which is ensured by assuming the compactness of the constraint set

reduced rank approximations to the far field transform in the gridded fast multipole method the fast multipole method fmm has been shown to have a reduced computational dependence on the size of finest level groups of elements when the elements are positioned on a regular grid and fft convolution is used to represent neighboring interactions however transformations between plane wave expansions used for fmm interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of fmm computations when finest level groups are large the transformation operators which are forward and inverse fourier transforms with the wave space confined to the unit sphere are smooth and well approximated using reduced rank decompositions that further reduce the computational dependence of the fmm on finest level group size the adaptive cross approximation aca is selected to represent the forward and adjoint far field transformation operators required by the fmm however the actual error of the aca is found to be greater than that predicted using traditional estimates and the aca generally performs worse than the approximation resulting from a truncated singular value decomposition svd to overcome these issues while avoiding the cost of a full scale svd the aca is employed with more stringent accuracy demands and recompressed using a reduced truncated svd the results show a greatly reduced approximation error that performs comparably to the full scale truncated svd without degrading the asymptotic computational efficiency associated with aca matrix assembly

zeroth order method for distributed optimization with approximate projections this paper studies the problem of minimizing a sum of possible nonsmooth convex functions that are corresponding to multiple interacting nodes subject to a convex state constraint set time varying directed network is considered here two types of computational constraints are investigated in this paper one where the information of gradients is not available and the other where the projection steps can only be calculated approximately we devise a distributed zeroth order method the implementation of which needs only functional evaluations and approximate projection in particular we show that the proposed method generates expected function value sequences that converge to the optimal value provided that the projection errors decrease at appropriate rates

distributed average consensus with dithered quantization in this paper we develop algorithms for distributed computation of averages of the node data over networks with bandwidth power constraints or large volumes of data distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted we propose a distributed algorithm in which the nodes utilize probabilistically quantized information i e dithered quantization to communicate with each other the algorithm we develop is a dynamical system that generates sequences achieving a consensus at one of the quantization values almost surely in addition we show that the expected value of the consensus is equal to the average of the original sensor data we derive an upper bound on the mean square error performance of the probabilistically quantized distributed averaging pqda moreover we show that the convergence of the pqda is monotonic by studying the evolution of the minimum length interval containing the node values we reveal that the length of this interval is a monotonically nonincreasing function with limit zero we also demonstrate that all the node values in the worst case converge to the final two quantization bins at the same rate as standard unquantized consensus finally we report the results of simulations conducted to evaluate the behavior and the effectiveness of the proposed algorithm in various scenarios

a second order multi agent network for bound constrained distributed optimization this technical note presents a second order multi agent network for distributed optimization with a sum of convex objective functions subject to bound constraints in the multi agent network the agents connect each others locally as an undirected graph and know only their own objectives and constraints the multi agent network is proved to be able to reach consensus to the optimal solution under mild assumptions moreover the consensus of the multi agent network is converted to the convergence of a dynamical system which is proved using the lyapunov method compared with existing multi agent networks for optimization the second order multi agent network herein is capable of solving more general constrained distributed optimization problems simulation results on two numerical examples are presented to substantiate the performance and characteristics of the multi agent network

a collective neurodynamic approach to distributed constrained optimization this paper presents a collective neurodynamic approach with multiple interconnected recurrent neural networks rnns for distributed constrained optimization the objective function of the distributed optimization problems to be solved is a sum of local convex objective functions which may be nonsmooth subject to its local constraints each local objective function is minimized individually by using an rnn with consensus among others in contrast to existing continuous time distributed optimization methods the proposed collective neurodynamic approach is capable of solving more general distributed optimization problems simulation results on three numerical examples are discussed to substantiate the effectiveness and characteristics of the proposed approach in addition an application to the optimal placement problem is delineated to demonstrate the viability of the approach

communication efficient algorithms for decentralized and stochastic optimization we present a new class of decentralized first order methods for nonsmooth and stochastic optimization problems defined over multiagent networks considering that communication is a major bottleneck in decentralized optimization our main goal in this paper is to develop algorithmic frameworks which can significantly reduce the number of inter node communications our major contribution is to present a new class of decentralized primal dual type algorithms namely the decentralized communication sliding dcs methods which can skip the inter node communications while agents solve the primal subproblems iteratively through linearizations of their local objective functions by employing dcs agents can find an epsilon solution both in terms of functional optimality gap and feasibility residual in mathcal o 1 epsilon resp mathcal o 1 sqrt epsilon communication rounds for general convex functions resp strongly convex functions while maintaining the mathcal o 1 epsilon 2 resp mathcal o 1 epsilon bound on the total number of intra node subgradient evaluations we also present a stochastic counterpart for these algorithms denoted by sdcs for solving stochastic optimization problems whose objective function cannot be evaluated exactly in comparison with existing results for decentralized nonsmooth and stochastic optimization we can reduce the total number of inter node communication rounds by orders of magnitude while still maintaining the optimal complexity bounds on intra node stochastic subgradient evaluations the bounds on the stochastic subgradient evaluations are actually comparable to those required for centralized nonsmooth and stochastic optimization under certain conditions on the target accuracy

distributed random convex programming via constraints consensus this paper discusses distributed approaches for the solution of random convex programs rcps rcps are convex optimization problems with a usually large number n of randomly extracted constraints they arise in several application areas especially in the context of decision making under uncertainty see g c calafiore siam j optim 20 2010 pp 3427 3464 g c calafiore and m c campi ieee trans automat control 51 2006 pp 742 753 we here consider a setup in which instances of the random constraints the scenario are not held by a single centralized processing unit but are instead distributed among different nodes of a network each node sees only a small subset of the constraints and may communicate with neighbors the objective is to make all nodes converge to the same solution as the centralized rcp problem to this end we develop two distributed algorithms that are variants of the constraints consensus algorithm g notarstefano and f bullo proceedings of the 46th iee

distributed continuous time convex optimization on weight balanced digraphs this technical note studies the continuous time distributed optimization of a sum of convex functions over directed graphs contrary to what is known in the consensus literature where the same dynamics works for both undirected and directed scenarios we show that the consensus based dynamics that solves the continuous time distributed optimization problem for undirected graphs fails to converge when transcribed to the directed setting this study sets the basis for the design of an alternative distributed dynamics which we show is guaranteed to converge on any strongly connected weight balanced digraph to the set of minimizers of a sum of convex differentiable functions with globally lipschitz gradients our technical approach combines notions of invariance and cocoercivity with the positive definiteness properties of graph matrices to establish the results

born iterative reconstruction using perturbed phase field estimates a method of image reconstruction from scattering measurements for use in ultrasonic imaging is presented the method employs distorted wave born iteration but does not require using a forward problem solver or solving large systems of equations these calculations are avoided by limiting intermediate estimates of medium variations to smooth functions in which the propagated fields can be approximated by phase perturbations derived from variations in a geometric path along rays the reconstruction itself is formed by a modification of the filtered backpropagation formula that includes correction terms to account for propagation through an estimated background numerical studies that validate the method for parameter ranges of interest in medical applications are presented the efficiency of this method offers the possibility of real time imaging from scattering measurements

distributed robust adaptive equilibrium computation for generalized convex games this paper considers a class of generalized convex games where each player is associated with a convex objective function a convex inequality constraint and a convex constraint set the players aim to compute a nash equilibrium through communicating with neighboring players the particular challenge we consider is that the component functions are unknown a priori to associated players we study two distributed computation algorithms and analyze their convergence properties in the presence of data transmission delays and dynamic changes of network topologies the algorithm performance is verified through demand response on the ieee 30 bus test system our technical tools integrate convex analysis variational inequalities and simultaneous perturbation stochastic approximation

a distributed simplex algorithm for degenerate linear programs and multi agent assignments in this paper we propose a novel distributed algorithm to solve degenerate linear programs on asynchronous peer to peer networks with distributed information structures we propose a distributed version of the well known simplex algorithm for general degenerate linear programs a network of agents running our algorithm will agree on a common optimal solution even if the optimal solution is not unique or will determine infeasibility or unboundedness of the problem we establish how the multi agent assignment problem can be efficiently solved by means of our distributed simplex algorithm we provide simulations supporting the conjecture that the completion time scales linearly with the diameter of the communication graph

using reciprocity to derive the far field displacements due to buried sources and scatterers it is shown that elastodynamic reciprocity provides a simpler approach for deriving the far field displacements due to buried sub surface sources in a half space compared with integral transform techniques the auxiliary fields employed in this approach are the fields associated with the reflection of plane waves of the three possible polarisations and the required far field can be expressed in terms of these well known auxiliary fields the crucial step in this approach is to evaluate a surface integral involving cross work terms between an outgoing spherical wavefront and the auxiliary fields consisting of incident and reflected plane waves this integral can be evaluated by the stationary phase approximation for the two dimensional case or by a generalisation of this approximation for the three dimensional case although this evaluation involves several distinct contributions the final result is shown to be very simple and it can be interpreted as a generalisation of a known result for the one d

distributed impulsive group consensus in second order multi agent systems under directed topology this paper investigates the impulsive group consensus problems of second order multi agent systems under directed network topology with acyclic partition two distributed impulsive sampled data protocols are presented to realise group consensus for both cases with leaders and leaderless and then some simple yet generic criteria on convergence for such algorithms are established it is shown that for the case with leaderless a feature of the present protocols is to give an explicit expression of group consensus states in terms of the initial values of the agents which allows us to develop a simple approach yielding the desired group or cluster consensus while for the case of virtual leaders a pinning like tracking technique is effectively designed to regulate all the agents access to the virtual leaders respectively for the purpose of practical control strategy finally simulation results are presented to illustrate the effectiveness of the theoretical analysis

distributed average consensus via gossip algorithm with real valued and quantized data for 0 q 1 this paper studies the problem of the gossip consensus algorithm with real valued and quantized data we study the effect of the mixing parameter on the convergence rate of the proposed gossip consensus algorithm and show when the proposed bounds are optimized with respect to the mixing parameter for a gossip consensus algorithm with quantized data we prove that it can achieve the consensus almost surely and the expected value of the final states is equal to the average of the initial states moreover we provide a result characterizing the convergence performance of the distance from consensus and make a comparison with the non quantized gossip consensus algorithm finally simulation results are provided to evaluate the effectiveness of the proposed algorithm

distributed dual averaging method for multi agent optimization with quantized communication abstract in this paper we propose a distributed dual averaging method for solving the constrained multi agent optimization problem in which multiple agents try to cooperatively optimize the sum of their local convex objective functions subject to a global convex constraint set over a network we consider two cases i the communications among agents are perfect and ii the communications among agents are deterministically or probabilistically quantized in the first case we provide a way to control the convergence performance of the proposed method through adjusting the number of consensus iterations we run in the subgradient step in the second case we consider two kinds of quantizers and provide bounds on their convergence rates to highlight the dependence on the quantization resolutions respectively finally we provide a numerical example to show the effectiveness of the proposed methods

constrained consensus algorithms with fixed step size for distributed convex optimization over multiagent networks in this technical note we are concerned with constrained consensus algorithms for distributed convex optimization with a sum of convex objective functions subject to local bound and equality constraints in multiagent networks each agent has its own data on objective function and constraints all the agents cooperatively find the minimizer while each agent can only communicate with its neighbors the consensus of multiagent networks with time invariant and undirected graphs is proven by the lyapunov method compared with existing consensus algorithms for distributed optimization with diminishing step sizes the proposed algorithms with fixed step size have better convergence rate simulation results on a numerical example are presented to substantiate the performance and characteristics of the proposed algorithms

speed of sound in pure water as a function of temperature in view of the adoption of the international temperature scale of 1990 its 90 which defines the international celsius temperatures t90 the dependence on temperature of the speed of sound in pure water is examined drawing on the experimental data published previously v a del grosso and c w mader speed of sound in pure water j acoust soc am 52 1442 1446 1972 it is found that the change from the previous t68 scale is significant at 100 c the difference between the two scales t68 t90 is 0 026 c resulting in a difference of 0 022 m s for the speed of sound the speed of sound is fitted to a new fifth order polynomial applicable over the t90 range 0 100 c

distributed gradient algorithm for constrained optimization with application to load sharing in power systems abstract in this paper a distributed constrained optimization problem is discussed to achieve the optimal point of the sum of agents local objective functions while satisfying local constraints here neither the local objective function nor local constraint functions of each agent can be shared with other agents to solve the problem a novel distributed continuous time algorithm is proposed by using the kkt condition combined with the lagrangian multiplier method and the convergence is proved with the help of lyapunov functions and an invariance principle for hybrid systems furthermore this distributed algorithm is applied to optimal load sharing control problem in power systems both theoretical and numerical results show that the optimal load sharing can be achieved within both generation and delivering constraints in a distributed way

focusing and imaging using eigenfunctions of the scattering operator an inverse scattering method that uses eigenfunctions of the scattering operator is presented this approach provides a unified framework that encompasses eigenfunction methods of focusing and quantitative image reconstruction in arbitrary media scattered acoustic fields are described using a compact normal operator the eigenfunctions of this operator are shown to correspond to the far field patterns of source distributions that are directly proportional to the position dependent contrast of a scattering object conversely the eigenfunctions of the scattering operator specify incident wave patterns that focus on these effective source distributions these focusing properties are employed in a new inverse scattering method that represents unknown scattering media using products of numerically calculated fields of eigenfunctions a regularized solution to the nonlinear inverse scattering problem is shown to result from combinations of these products so that the products comprise a natural basis for efficient and accurate reconstructions of unknown inhomogeneities the corresponding linearized problem is solved analytically resulting in a simple formula for the low pass filtered scattering potential the linear formula is analytically equivalent to known filtered backpropagation formulas for born inversion and at least in the case of small scattering objects has advantages of computational simplicity and efficiency a similarly efficient and simple formula is derived for the nonlinear problem in which the total acoustic pressure can be determined based on an estimate of the medium computational results illustrate focusing of eigenfunctions on discrete and distributed scattering media quantitative imaging of inhomogeneous media using products of retransmitted eigenfunctions inverse scattering in an inhomogeneous background medium and reconstructions for data corrupted by noise

on the optimal parameter of the composite laplacian quadratics function abstract recently the composite quadratic lyapunov function has been extended to study of multi agent systems leading to the so called composite laplacian quadratics clqs function compared with quadratic lyapunov functions the clqs function can yield a larger convergence region and is particularly useful in stabilization of multi agent systems with complex dynamics such as differential inclusions in the definition of the clqs function an optimal vector parameter plays a critical role in determining the value of the clqs function and in constructing stabilization laws derived from the clqs function this paper focuses on the properties of the optimal parameter of the clqs function the uniqueness of the optimal parameter is established a distributed computation approach is further proposed which is useful in computing the optimal parameter the robustness issue of the optimal parameter is also investigated for a multi agent system described by linear differential inclusions finally a numerical example is provided to validate the proposed theoretical results

on distributed convex optimization under inequality and equality constraints we consider a general multi agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint a global equality constraint and a global constraint set the objective function is defined by a sum of local objective functions while the global constraint set is produced by the intersection of local constraint sets in particular we study two cases one where the equality constraint is absent and the other where the local constraint sets are identical we devise two distributed primal dual subgradient algorithms based on the characterization of the primal dual optimal solutions as the saddle points of the lagrangian and penalty functions these algorithms can be implemented over networks with dynamically changing topologies but satisfying a standard connectivity property and allow the agents to asymptotically agree on optimal solutions and optimal values of the optimization problem under the slater s condition

on the consensus of homogeneous multi agent systems with arbitrarily switching topology abstract in this paper we investigate the consensus problem under arbitrary switching for homogeneous multi agent systems with switching communication topology by assuming that each agent is described by a single input stabilizable state space model and that the communication graph is connected at every time instant under these assumptions we construct a common quadratic positive definite lyapunov function for the switched system describing the evolution of the disagreement vector thus showing that the agents always reach consensus in addition the proof leads to the explicit construction of a constant state feedback matrix that allows the multi agent system to achieve consensus

infinite words with linear subword complexity abstract in section 1 we study the relations among some combinatorial properties of infinite words especially in the case of infinite words with linear subword complexity the main result of section 1 concerns a permutation property of infinite words with linear complexity in section 2 we investigate the special case of the sturmian infinite words the main result is that a sturmian infinite word associated to a real number contains no k th powers iff has a continued fraction expansion with bounded partial quotients in section 3 it is shown that some of the results of sections 1 and 2 are optimal

average consensus in networks of dynamic agents with switching topologies and multiple time varying delays in this paper we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time varying communication delays by employing a linear matrix inequality method we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected particularly several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying communication delays numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results

consensus in time delayed multi agent systems with quantized dwell times abstract this paper investigates the effects of quantized dwell times in solving consensus problems in time delayed multi agent systems with the asynchronous property of unpredictable quantization jumps in inter agent communications the quantized dwell times can be introduced on purpose or be inherent from quantizing devices they beneficially avoid undesirable fast chattering of quantizers outputs and mathematical difficulties in convergence analysis the main result shows that the largest eigenvalue of the interaction graph laplacian well characterizes the dependence of maximum allowable time delay on quantized dwell times and quantizer parameters under the assumption of heterogeneous time varying transmission delays simulations are presented to show the effectiveness of the main result

optimal focusing by spatio temporal inverse filter i basic principles a focusing technique based on the inversion of the propagation operator relating an array of transducers to a set of control points inside a medium was proposed in previous work tanter et al j acoust soc am 108 223 234 2000 and is extended here to the time domain as the inversion of the propagation operator is achieved both in space and time this technique allows calculation of the set of temporal signals to be emitted by each element of the array in order to optimally focus on a chosen control point this broadband inversion process takes advantage of the singular value decomposition of the propagation operator in the fourier domain the physical meaning of this decomposition is explained in a homogeneous medium in particular a definition of the number of degrees of freedom necessary to define the acoustic field generated by an array of limited aperture in a focal plane of limited extent is given this number corresponds to the number of independent signals that can be created in the focal area both in space and time in this paper this broadband inverse focusing technique is compared in homogeneous media with the classical focusing achieved by simple geometrical considerations but also with time reversal focusing it is shown that even in a simple medium slight differences appear between these three focusing strategies in the companion paper aubry et al j acoust soc am 110 48 58 2001 the three focusing techniques are compared in heterogeneous absorbing or complex media where classical focusing is strongly degraded the strong improvement achieved by the spatio temporal inverse filter technique emphasizes the great potential of multiple channel systems having the ability to apply completely different signal waveforms on each transducer of the array the application of this focusing technique could be of great interest in various ultrasonic fields such as medical imaging nondestructive testing and underwater acoustics

inexact dual averaging method for distributed multi agent optimization abstract we consider a distributed convex optimization problem over a network where multiple agents collectively try to minimize a sum of local convex functions of the same variables each of which is available to one specific agent only for solving this optimization problem we present an inexact version of the dual averaging method this extends recent results of duchi 2012 which cover the error free case to the case where an error is present in calculating the subgradient of the objective function or in computing the projection we show that when the errors decrease at appropriate rates our method achieves the same convergence rate as in the error free case in particular the convergence of the method is also established for nonsummable errors we also provide numerical results to validate the theoretic results

distributed convergence to nash equilibria in two network zero sum games this paper considers a class of strategic scenarios in which two networks of agents have opposing objectives with regard to the optimization of a common objective function in the resulting zero sum game individual agents collaborate with neighbors in their respective network and have only partial knowledge of the state of the agents in the other network for the case when the interaction topology of each network is undirected we synthesize a distributed saddle point strategy and establish its convergence to the nash equilibrium for the class of strictly concave convex and locally lipschitz objective functions we also show that this dynamics does not converge in general if the topologies are directed this justifies the introduction in the directed case of a generalization of this distributed dynamics which we show converges to the nash equilibrium for the class of strictly concave convex differentiable functions with globally lipschitz gradients the technical approach combines tools from algebraic graph theory nonsmooth analysis set valued dynamical systems and game theory

distributed constrained optimal consensus of multi agent systems we study a distributed optimal consensus problem of continuous time multi agent systems with a common state set constraint each agent is assigned with an individual cost function which is coercive and convex a distributed control protocol is to be designed to guarantee a consensus and in the meanwhile reach the minimizer of the aggregate cost functions within the constraint set three terms are included in the protocol local averaging local projection and local subgradient with a diminishing but persistent gain it is shown that the constrained optimal consensus can be achieved under a uniformly jointly connected communication network with bounded time varying edge weights

distributed adaptive output consensus control of a class of heterogeneous multi agent systems under switching directed topologies in this paper we consider a leader follower output consensus problem for a class of uncertain heterogeneous non affine pure feedback multi agent systems mass in the presence of time delay items and input saturation restrictions under switching directed topologies a distributed adaptive control scheme is constructed by combining lyapunov krasovskii functionals backstepping methods neural networks nns auxiliary systems graph theory the mean value theorem and the implicit function theory along with the dynamic surface control dsc technique the key advantages of the designed control approach are that there is no requirement of precise knowledge about uncertain dynamics and time delay items of individual agents and the computational burden can drastically be reduced by employing the dsc technique also norms of unknown weight of neural networks are estimated online instead of weight vectors themselves in theory it can be proven that the output signals of follower agents can synchronize with the leader s and all signals in the closed loop system are cooperatively semiglobally uniformly ultimately bounded csuub by suitable choice of design parameters two simulation examples are presented to demonstrate the effectiveness of the proposed strategy

the deformed consensus protocol this paper studies a generalization of the standard continuous time consensus protocol obtained by replacing the laplacian matrix of the communication graph with the so called deformed laplacian the deformed laplacian is a second degree matrix polynomial in the real variable s which reduces to the standard laplacian for s equal to unity the stability properties of the ensuing deformed consensus protocol are studied in terms of parameter s for some special families of undirected and directed graphs and for arbitrary graph topologies by leveraging the spectral theory of quadratic eigenvalue problems examples and simulation results are provided to illustrate our theoretical findings

distributed constrained optimization by consensus based primal dual perturbation method various distributed optimization methods have been developed for solving problems which have simple local constraint sets and whose objective function is the sum of local cost functions of distributed agents in a network motivated by emerging applications in smart grid and distributed sparse regression this paper studies distributed optimization methods for solving general problems which have a coupled global cost function and have inequality constraints we consider a network scenario where each agent has no global knowledge and can access only its local mapping and constraint functions to solve this problem in a distributed manner we propose a consensus based distributed primal dual perturbation pdp algorithm in the algorithm agents employ the average consensus technique to estimate the global cost and constraint functions via exchanging messages with neighbors and meanwhile use a local primal dual perturbed subgradient method to approach a global optimum the proposed pdp method not only can handle smooth inequality constraints but also non smooth constraints such as some sparsity promoting constraints arising in sparse optimization we prove that the proposed pdp algorithm converges to an optimal primal dual solution of the original problem under standard problem and network assumptions numerical results illustrating the performance of the proposed algorithm for a distributed demand response control problem in smart grid are also presented

homogeneous networks of non introspective agents under external disturbances h almost synchronization this paper addresses the problem of h almost synchronization for homogeneous networks of general linear agents subject to external disturbances and under directional communication links agents are presumed to be non introspective i e agents are not aware of their own states or outputs and the only available information for each agent is a network measurement that is a linear combination of relative outputs under a certain set of conditions a family of dynamic protocols is developed such that the impact of disturbances on the synchronization error dynamics expressed in terms of the h norm of the corresponding closed loop transfer function is reduced to any arbitrarily small value

quantized consensus on first order integrator networks abstract this paper studies the quantized average consensus problem of first order integrator agents with connected undirected communication graphs because quantized data is inherently associated with discrete time measurements a sampled data based average consensus protocol is proposed in which each agent uses the quantized states of its neighbors measured synchronously at sampling times to update its own state it is proved that for a connected network the distance between the individual state and the average of initial states becomes smaller than the quantization step size in finite time provided the sampling size is smaller than a constant depending on the degree of the communication topology when the sampling size tends to zero an asynchronous protocol is investigated in which the limitation of the switching frequency of quantizers is considered it is shown that for a connected network the given protocol drives the state of each agent into a neighborhood of the average of initial states provided the dwell time of quantizers is small enough

distributed averaging on digital erasure networks iterative distributed algorithms are studied for computing arithmetic averages over networks of agents connected through memoryless broadcast erasure channels these algorithms do not require the agents to have any knowledge about the global network structure or size almost sure convergence to state agreement is proved and the communication and computational complexities of the algorithms are analyzed both the number of transmissions and the number of computations performed by each agent of the network are shown to grow not faster than poly logarithmically in the desired precision the impact of the graph topology on the algorithms performance is analyzed as well moreover it is shown how in the presence of noiseless communication feedback one can modify the algorithms significantly improving their performance versus complexity trade off

quantitative imaging using a time domain eigenfunction method an inverse scattering method that uses eigenfunctions of a scattering operator at a single frequency is extended to include the full range of frequencies present in the incident pulse waveform the resulting so called time domain eigenfunction method is shown to yield a modulated version of the scattering potential the potential is recovered by a demodulation process using cross correlation with a reference including an adaptive delay in the reference is shown to compensate partially for the linearization of the born approximation and to extend its valid range the k space window of the time domain solution is expressed in terms of the incident waveform and shown to be smoother than that of a single frequency solution the time domain method is examined using both calculated and measured data in the calculations an exact solution for scattering from one or multiple nonconcentric cylinders is used to obtain the scattered field in the measurements a novel ring transducer system was employed to obtain the incident and total fields the results of simulations and experiments show that the method is robust and accurate for the size of objects considered and that the point resolution approaches one half the wavelength at the pulse center frequency

constrained consensus and optimization in multi agent networks we present distributed algorithms that can be used by multiple agents to align their estimates with a particular value over a network with time varying connectivity our framework is general in that this value can represent a consensus value among multiple agents or an optimal solution of an optimization problem where the global objective function is a combination of local agent objective functions our main focus is on constrained problems where the estimates of each agent are restricted to lie in different convex sets to highlight the effects of constraints we first consider a constrained consensus problem and present a distributed projected consensus algorithm in which agents combine their local averaging operation with projection on their individual constraint sets this algorithm can be viewed as a version of an alternating projection method with weights that are varying over time and across agents we establish convergence and convergence rate results for the projected consensus algorithm we next study a constrained optimization problem for optimizing the sum of local objective functions of the agents subject to the intersection of their local constraint sets we present a distributed projected subgradient algorithm which involves each agent performing a local averaging operation taking a subgradient step to minimize its own objective function and projecting on its constraint set we show that with an appropriately selected stepsize rule the agent estimates generated by this algorithm converge to the same optimal solution for the cases when the weights are constant and equal and when the weights are time varying but all agents have the same constraint set

ultrasound tomography for simultaneous reconstruction of acoustic density attenuation and compressibility profiles a fast and efficient forward scattering solver is developed for use in ultrasound tomography the solver is formulated so as to enable the calculation of scattering from large and relatively high contrast objects with inhomogeneous physical properties that vary simultaneously in acoustic attenuation compressibility and density it is based on the method of moments in conjunction with a novel implementation of the conjugate gradient algorithm which requires the use of the adjoints of the scattering operators the solver takes advantage of the symmetric block toeplitz matrix with symmetric toeplitz blocks property of the green s function matrix to increase efficiency and only stores the first row of this matrix to reduce memory requirements this row is then used for the matrix vector multiplication using the fast fourier transform technique thus resulting in the computational complexity of o n log n the marching on source technique is also used to provide a good initial guess which allows the conjugate gradient technique to converge faster than initializing with an arbitrary guess this feature is important in tomographic inversion algorithms which require that the object to be imaged be interrogated via several incident fields forward scattering and inversion examples based on the conjugate gradient least squares regularized born iterative method are shown in two dimensions for objects varying in all three physical properties

decentralized estimation in an inhomogeneous sensing environment we consider decentralized estimation of a noise corrupted deterministic parameter by a bandwidth constrained sensor network with a fusion center the sensor noises are assumed to be additive zero mean spatially uncorrelated but otherwise unknown and possibly different across sensors due to varying sensor quality and inhomogeneous sensing environment the classical best linear unbiased estimator blue linearly combines the real valued sensor observations to minimize the mean square error mse unfortunately such a scheme cannot be implemented in a practical bandwidth constrained sensor network due to its requirement to transmit real valued messages in this paper we construct a decentralized estimation scheme des where each sensor compresses its observation to a small number of bits with length proportional to the logarithm of its local signal to noise ratio snr the resulting compressed bits from different sensors are then collected and combined by the fusion center to estimate the unknown parameter the proposed des is universal in the sense that each sensor compression scheme requires only the knowledge of local snr rather than the noise probability distribution functions pdf while the final fusion step is also independent of the local noise pdfs we show that the mse of the proposed des is within a constant factor of 25 8 of that achieved by the classical centralized blue estimator

a necessary and sufficient condition for consensus over random networks we consider the consensus problem for stochastic discrete time linear dynamical systems the underlying graph of such systems at a given time instance is derived from a random graph process independent of other time instances for such a framework we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments this easily verifiable condition uses the spectrum of the average weight matrix finally we investigate a special case for which the linear dynamical system converges to a fixed vector with probability 1

dual decomposition for multi agent distributed optimization with coupling constraints abstract we study distributed optimization in a cooperative multi agent setting where agents have to agree on the usage of shared resources and can communicate via a time varying network to this purpose each agent has its own decision variables that should be set so as to minimize its individual objective function subject to local constraints resource sharing is modeled via coupling constraints that involve the non positivity of the sum of agents individual functions each one depending on the decision variables of one single agent we propose a novel distributed algorithm to minimize the sum of the agents objective functions subject to both local and coupling constraints where dual decomposition and proximal minimization are combined in an iterative scheme notably privacy of information is guaranteed since only the dual optimization variables associated with the coupling constraints are exchanged by the agents under convexity assumptions jointly with suitable connectivity properties of the communication network we are able to prove that agents reach consensus to some optimal solution of the centralized dual problem counterpart while primal variables converge to the set of optimizers of the centralized primal problem the efficacy of the proposed approach is demonstrated on a plug in electric vehicles charging problem

distributed convex optimization via continuous time coordination algorithms with discrete time communication this paper proposes a novel class of distributed continuous time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents we establish the exponential convergence of the proposed algorithm under i strongly connected and weight balanced digraph topologies when the local costs are strongly convex with globally lipschitz gradients and ii connected graph topologies when the local costs are strongly convex with locally lipschitz gradients when the local cost functions are convex and the global cost function is strictly convex we establish asymptotic convergence under connected graph topologies we also characterize the algorithm s correctness under time varying interaction topologies and study its privacy preservation properties motivated by practical considerations we analyze the algorithm implementation with discrete time communication we provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication building on this result we design a provably correct centralized event triggered communication scheme that is free of zeno behavior finally we develop a distributed asynchronous event triggered communication scheme that is also free of zeno with asymptotic convergence guarantees several simulations illustrate our results

multi vehicle consensus with a time varying reference state in this paper we study the consensus problem in multi vehicle systems where the information states of all vehicles approach a time varying reference state under the condition that only a portion of the vehicles e g the unique team leader have access to the reference state and the portion of the vehicles might not have a directed path to all of the other vehicles in the team we first analyze a consensus algorithm with a constant reference state using graph theoretical tools we then propose consensus algorithms with a time varying reference state and show necessary and sufficient conditions under which consensus is reached on the time varying reference state the time varying reference state can be an exogenous signal or evolve according to a nonlinear model these consensus algorithms are also extended to achieve relative state deviations among the vehicles an application example to multi vehicle formation control is given as a proof of concept

convergence rates of distributed nesterov like gradient methods on random networks we consider distributed optimization in random networks where n nodes cooperatively minimize the sum i 1n fi x of their individual convex costs existing literature proposes distributed gradient like methods that are computationally cheap and resilient to link failures but have slow convergence rates in this paper we propose accelerated distributed gradient methods that 1 are resilient to link failures 2 computationally cheap and 3 improve convergence rates over other gradient methods we model the network by a sequence of independent identically distributed random matrices w k drawn from the set of symmetric stochastic matrices with positive diagonals the network is connected on average and the cost functions are convex differentiable with lipschitz continuous and bounded gradients we design two distributed nesterov like gradient methods that modify the d ng and d nc methods that we proposed for static networks we prove their convergence rates in terms of the expected optimality gap at the cost function let k and k be the number of per node gradient evaluations and per node communications respectively then the modified d ng achieves rates o logk k and o logk k and the modified d nc rates o 1 k2 and o 1 k2 where 0 is arbitrarily small for comparison the standard distributed gradient method cannot do better than 1 k2 3 and 1 k2 3 on the same class of cost functions even for static networks simulation examples illustrate our analytical findings

primal dual subgradient methods for convex problems in this paper we present a new approach for constructing subgradient schemes for different types of nonsmooth problems with convex structure our methods are primal dual since they are always able to generate a feasible approximation to the optimum of an appropriately formulated dual problem besides other advantages this useful feature provides the methods with a reliable stopping criterion the proposed schemes differ from the classical approaches divergent series methods mirror descent methods by presence of two control sequences the first sequence is responsible for aggregating the support functions in the dual space and the second one establishes a dynamically updated scale between the primal and dual spaces this additional flexibility allows to guarantee a boundedness of the sequence of primal test points even in the case of unbounded feasible set however we always assume the uniform boundedness of subgradients we present the variants of subgradient schemes for nonsmooth convex minimization minimax problems saddle point problems variational inequalities and stochastic optimization in all situations our methods are proved to be optimal from the view point of worst case black box lower complexity bounds

gossip algorithms for convex consensus optimization over networks in many applications nodes in a network desire not only a consensus but an optimal one to date a family of subgradient algorithms have been proposed to solve this problem under general convexity assumptions this technical note shows that for the scalar case and by assuming a bit more novel non gradient based algorithms with appealing features can be constructed specifically we develop pairwise equalizing pe and pairwise bisectioning pb two gossip algorithms that solve unconstrained separable convex consensus optimization problems over undirected networks with time varying topologies where each local function is strictly convex continuously differentiable and has a minimizer we show that pe and pb are easy to implement bypass limitations of the subgradient algorithms and produce switched nonlinear networked dynamical systems that admit a common lyapunov function and asymptotically converge moreover pe generalizes the well known pairwise averaging and randomized gossip algorithm while pb relaxes a requirement of pe allowing nodes to never share their local functions

a multi agent system with a proportional integral protocol for distributed constrained optimization this technical note presents a continuous time multi agent system for distributed optimization with an additive objective function composed of individual objective functions subject to bound equality and inequality constraints each individual objective function is assumed to be convex in the region defined by its local bound constraints only without the need to be globally convex all agents in the system communicate using a proportional integral protocol with their output information instead of state information to reduce communication bandwidth it is proved that all agents with any initial state can reach output consensus at an optimal solution to the given constrained optimization problem provided that the graph describing the communication links among agents is undirected and connected it is further proved that the system with only integral protocol is also convergent to the unique optimal solution if each individual objective function is strictly convex simulation results are presented to substantiate the theoretical results

note on powers in three interval exchange transformations we study repetitions in infinite words coding exchange of three intervals with permutation 3 2 1 called 3iet words the language of such words is determined by two parameters e we show that finiteness of the index of 3iet words is equivalent to boundedness of the coefficients of the continued fraction of e in this case we also give an upper and a lower estimate on the index of the corresponding 3iet word our main tool is the connection between a 3iet word with parameters e and sturmian words with slope e

linear convergence rate of a class of distributed augmented lagrangian algorithms we study distributed optimization where nodes cooperatively minimize the sum of their individual locally known convex costs f i x s x in bbr d is global distributed augmented lagrangian al methods have good empirical performance on several signal processing and learning applications but there is limited understanding of their convergence rates and how it depends on the underlying network this paper establishes globally linear geometric convergence rates of a class of deterministic and randomized distributed al methods when the f i s are twice continuously differentiable and have a bounded hessian we give explicit dependence of the convergence rates on the underlying network parameters simulations illustrate our analytical findings

convergence speed in distributed consensus and averaging we study the convergence speed of distributed iterative algorithms for the consensus and averaging problems with emphasis on the latter we first consider the case of a fixed communication topology we show that a simple adaptation of a consensus algorithm leads to an averaging algorithm we prove lower bounds on the worst case convergence time for various classes of linear time invariant distributed consensus methods and provide an algorithm that essentially matches those lower bounds we then consider the case of a time varying topology and provide a polynomial time averaging algorithm

scattering calculation and image reconstruction using elevation focused beams pressure scattered by cylindrical and spherical objects with elevation focused illumination and reception has been analytically calculated and corresponding cross sections have been reconstructed with a two dimensional algorithm elevation focusing was used to elucidate constraints on quantitative imaging of three dimensional objects with two dimensional algorithms focused illumination and reception are represented by angular spectra of plane waves that were efficiently computed using a fourier interpolation method to maintain the same angles for all temporal frequencies reconstructions were formed using an eigenfunction method with multiple frequencies phase compensation and iteration the results show that the scattered pressure reduces to a two dimensional expression and two dimensional algorithms are applicable when the region of a three dimensional object within an elevation focused beam is approximately constant in elevation the results also show that energy scattered out of the reception aperture by objects contained within the focused beam can result in the reconstructed values of attenuation slope being greater than true values at the boundary of the object reconstructed sound speed images however appear to be relatively unaffected by the loss in scattered energy the broad conclusion that can be drawn from these results is that two dimensional reconstructions require compensation to account for uncaptured three dimensional scattering

nash equilibrium computation in subnetwork zero sum games with switching communications in this paper we investigate a distributed nash equilibrium computation problem for a time varying multi agent network consisting of two subnetworks where the two subnetworks share the same objective function we first propose a subgradient based distributed algorithm with heterogeneous stepsizes to compute a nash equilibrium of a zero sum game we then prove that the proposed algorithm can achieve a nash equilibrium under uniformly jointly strongly connected ujsc weight balanced digraphs with homogenous stepsizes moreover we demonstrate that for weighted unbalanced graphs a nash equilibrium may not be achieved with homogenous stepsizes unless certain conditions on the objective function hold we show that there always exist heterogeneous stepsizes for the proposed algorithm to guarantee that a nash equilibrium can be achieved for ujsc digraphs finally in two standard weight unbalanced cases we verify the convergence to a nash equilibrium by adaptively updating the stepsizes along with the arc weights in the proposed algorithm

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

second order consensus of networked thrust propelled vehicles on directed graphs this technical note addresses the second order consensus problem of multiple underactuated thrust propelled vehicles tpvs on directed graphs containing a directed spanning tree we propose an adaptive control approach to resolve this problem and the proposed controller does not rely on the commonly used backstepping methodology and the exact knowledge of the mass properties of the tpvs in addition the resultant complexity is reduced and the requirement on the interaction graph is relaxed using an input output analysis we show that the proposed controller realizes second order consensus of the tpvs i e the position and velocity consensus errors between the tpvs converge to zero and moreover the velocities of the tpvs converge to the weighted average of their initial values the performance of the proposed control approach is shown by a numerical simulation

a computational study of reconstruction algorithms for diffraction tomography interpolation versus filtered backpropagation from the standpoint of reporting a new contribution this paper shows that by using bilinear interpolation followed by direct two dimensional fourier inversion one can obtain reconstructions of quality which is comparable to that produced by the filtered backpropagation algorithm proposed recently by devaney for an n n image reconstructed from n diffracted projections the former approach requires approximately 4n fft s whereas the backpropagation technique requires approximately n2fft s we have also taken this opportunity to present the reader with a tutorial introduction to diffraction tomography an area that is becoming increasingly important not only in medical imaging but also in underwater and seismic mapping with microwaves and sound the main feature of the tutorial part is the statement of the fourier diffraction projection theorem which is an extension of the traditional fourier slice theorem to the case of image formation with diffracting illumination

extensions of fast lipschitz optimization the need of fast distributed solvers for optimization problems in networked systems has motivated the recent development of the fast lipschitz optimization framework in such an optimization problems satisfying certain qualifying conditions such as monotonicity of the objective function and contractivity of the constraints have a unique optimal solution obtained via fast distributed algorithms that compute the fixed point of the constraints this paper extends the set of problems for which the fast lipschitz framework applies existing assumptions on the problem form are relaxed and new and generalized qualifying conditions are established by novel results based on lagrangian duality it is shown for which cases of more constraints than decision variables and less constraints than decision variables fast lipschitz optimization applies new results are obtained by imposing non strict monotonicity of the objective functions the extended fast lipschitz framework is illustrated by a number of examples including network optimization and optimal control problems

distributed consensus algorithms in sensor networks quantized data and random link failures the paper studies the problem of distributed average consensus in sensor networks with quantized data and random link failures to achieve consensus dither small noise is added to the sensor states before quantization when the quantizer range is unbounded countable number of quantizer levels stochastic approximation shows that consensus is asymptotically achieved with probability one and in mean square to a finite random variable we show that the mean squared error mse can be made arbitrarily small by tuning the link weight sequence at a cost of the convergence rate of the algorithm to study dithered consensus with random links when the range of the quantizer is bounded we establish uniform boundedness of the sample paths of the unbounded quantizer this requires characterization of the statistical properties of the supremum taken over the sample paths of the state of the quantizer this is accomplished by splitting the state vector of the quantizer in two components one along the consensus subspace and the other along the subspace orthogonal to the consensus subspace the proofs use maximal inequalities for submartingale and supermartingale sequences from these we derive probability bounds on the excursions of the two subsequences from which probability bounds on the excursions of the quantizer state vector follow the paper shows how to use these probability bounds to design the quantizer parameters and to explore tradeoffs among the number of quantizer levels the size of the quantization steps the desired probability of saturation and the desired level of accuracy away from consensus finally the paper illustrates the quantizer design with a numerical study

distributed and recursive parameter estimation in parametrized linear state space models we consider a network of sensors deployed to sense a spatio temporal field and infer parameters of interest about the field we are interested in the case where each sensor s observation sequence is modeled as a state space process that is perturbed by random noise and the models across sensors are parametrized by the same parameter vector the sensors collaborate to estimate this parameter from their measurements and to this end we propose a distributed and recursive estimation algorithm which we refer to as the incremental recursive prediction error algorithm this algorithm has the distributed property of incremental gradient algorithms and the on line property of recursive prediction error algorithms

quantized consensus over directed networks with switching topologies abstract this paper studies the quantized consensus problem for a group of agents over directed networks with switching topologies we propose an effective distributed protocol with an adaptive finite level uniform quantized strategy under which consensus among agents is guaranteed with weaker communication conditions in particular we analytically prove that each agent sending 5 level quantized information to each of its neighbors together with 3 level quantized information to itself at each time step which suffices for attaining consensus with an exponential convergence rate as long as the duration of all link failures in the directed network is bounded by dropping the typical common left eigenvector requirement for the existence of common quadratic lyapunov function we conduct the convergence analysis based on the notion of input to output stability the proposed quantized protocol has favorable merits of requiring little communication overhead and increasing robustness to link unreliability and it fits well into the digital network framework

distributed algorithms for reaching consensus on general functions this paper presents analysis and design results for distributed consensus algorithms in multi agent networks we consider continuous consensus functions of the initial state of the network agents under mild smoothness assumptions we obtain necessary and sufficient conditions characterizing any algorithm that asymptotically achieves consensus this characterization is the building block to obtain various design results for networks with weighted directed interconnection topologies we first identify a class of smooth functions for which one can synthesize in a systematic way distributed algorithms that achieve consensus we apply this result to the family of weighted power mean functions and characterize the exponential convergence properties of the resulting algorithms we establish the validity of these results for scenarios with switching interconnection topologies finally we conclude with two discontinuous distributed algorithms that achieve respectively max and min consensus in finite time

distributed adaptive convex optimization on directed graphs via continuous time algorithms this note considers the distributed optimization problem on directed graphs with nonconvex local objective functions and the unknown network connectivity a new adaptive algorithm is proposed to minimize a differentiable global objective function by introducing dynamic coupling gains and updating the coupling gains using relative information of system states the nonconvexity of local objective functions unknown network connectivity and the uncertain dynamics caused by locally lipschitz gradients are tackled concurrently consequently the global asymptotic convergence is established when the global objective function is strongly convex and the gradients of local objective functions are only locally lipschitz when the communication graph is strongly connected and weight balanced the algorithm is independent of any global information then the algorithm is naturally extended to unbalanced directed graphs by using the left eigenvector of the laplacian matrix associated with the zero eigenvalue several numerical simulations are presented to verify the results

convergence rate analysis of distributed optimization with projected subgradient algorithm abstract in this paper we revisit the consensus based projected subgradient algorithm proposed for a common set constraint we show that the commonly adopted non summable and square summable diminishing step sizes of subgradients can be relaxed to be only non summable if the constrained optimum set is bounded more importantly for a strongly convex aggregate cost with different types of step sizes we provide a systematical analysis to derive the asymptotic upper bound of convergence rates in terms of the optimum residual and select the best step sizes accordingly our result shows that a convergence rate of o 1 k can be achieved with a step size o 1 k

fast distributed gradient methods we study distributed optimization problems when n nodes minimize the sum of their individual costs subject to a common vector variable the costs are convex have lipschitz continuous gradient with constant l and bounded gradient we propose two fast distributed gradient algorithms based on the centralized nesterov gradient algorithm and establish their convergence rates in terms of the per node communications k and the per node gradient evaluations k our first method distributed nesterov gradient achieves rates o logk k and o logk k our second method distributed nesterov gradient with consensus iterations assumes at all nodes knowledge of l and w the second largest singular value of the n n doubly stochastic weight matrix w it achieves rates o 1 k2 and o 1 k2 0 arbitrarily small further we give for both methods explicit dependence of the convergence constants on n and w simulation examples illustrate our findings

the fast multipole method and fourier convolution for the solution of acoustic scattering on regular volumetric grids the fast multipole method fmm is applied to the solution of large scale three dimensional acoustic scattering problems involving inhomogeneous objects defined on a regular grid the grid arrangement is especially well suited to applications in which the scattering geometry is not known a priori and is reconstructed on a regular grid using iterative inverse scattering algorithms or other imaging techniques the regular structure of unknown scattering elements facilitates a dramatic reduction in the amount of storage and computation required for the fmm both of which scale linearly with the number of scattering elements in particular the use of fast fourier transforms to compute green s function convolutions required for neighboring interactions lowers the often significant cost of finest level fmm computations and helps mitigate the dependence of fmm cost on finest level box size numerical results demonstrate the efficiency of the composite method as the number of scattering elements in each finest level box is increased

distributed optimal in network resource allocation algorithm design via a control theoretic approach abstract in this paper we consider an in network optimal resource allocation problem with multiple demand equations we propose a novel distributed continuous time algorithm that solves the problem over strongly connected and weight balanced digraph network topologies when the local cost functions are strongly convex we also discuss the extension of our convergence guarantees to dynamically changing topologies finally we show that if the network is an undirected connected graph we can guarantee stability and convergence of our algorithm for problems involving local convex functions this convergence guarantee is to a point in the set of minimizers of our optimal resource allocation problem the design and analysis of our algorithm are carried out using a control theoretic approach we demonstrate our results through a numerical example

nonlinear diffractive inverse scattering for multiple scattering in inhomogeneous acoustic background media this paper discusses a nonlinear diffractive inversion of the helmholtz equation for multiscattering configurations where the scatterers are embedded in an inhomogeneous background medium using the finite element model to iteratively compute the scattered field in conjunction with a novel discrete cosine transform dct representation of the object function permits the development of an efficient nonlinear inversion algorithm the object function expansion is obtained by applying the dct to sampling points which are chosen at the zeros of the chebyshev polynomials and achieves an accuracy comparable to the more popular sinc basis with far fewer expansion terms after the inverse scattering formulation is converted into a nonlinear parameter estimation problem the final matrix equation is linearized and solved by a standard least squares algorithm several examples of two dimensional single and multiple scattering configurations for both homogeneous and inhomogeneous acoustic backgrounds will illustra

randomized gradient free method for multiagent optimization over time varying networks in this brief we consider the multiagent optimization over a network where multiple agents try to minimize a sum of nonsmooth but lipschitz continuous functions subject to a convex state constraint set the underlying network topology is modeled as time varying we propose a randomized derivative free method where in each update the random gradient free oracles are utilized instead of the subgradients sgs in contrast to the existing work we do not require that agents are able to compute the sgs of their objective functions we establish the convergence of the method to an approximate solution of the multiagent optimization problem within the error level depending on the smoothing parameter and the lipschitz constant of each agent s objective function finally a numerical example is provided to demonstrate the effectiveness of the method

stochastic strongly convex optimization via distributed epoch stochastic gradient algorithm this article considers the problem of stochastic strongly convex optimization over a network of multiple interacting nodes the optimization is under a global inequality constraint and the restriction that nodes have only access to the stochastic gradients of their objective functions we propose an efficient distributed non primal dual algorithm by incorporating the inequality constraint into the objective via a smoothing technique we show that the proposed algorithm achieves an optimal o 1 t t is the total number of iterations convergence rate in the mean square distance from the optimal solution in particular we establish a high probability bound for the proposed algorithm by showing that with a probability at least 1 the proposed algorithm converges at a rate of o ln ln t t finally we provide numerical experiments to demonstrate the efficacy of the proposed algorithm

fast inverse scattering solutions using the distorted born iterative method and the multilevel fast multipole algorithm the distorted born iterative method dbim computes iterative solutions to nonlinear inverse scattering problems through successive linear approximations by decomposing the scattered field into a superposition of scattering by an inhomogeneous background and by a material perturbation large or high contrast variations in medium properties can be imaged through iterations that are each subject to the distorted born approximation however the need to repeatedly compute forward solutions still imposes a very heavy computational burden to ameliorate this problem the multilevel fast multipole algorithm mlfma has been applied as a forward solver within the dbim the mlfma computes forward solutions in linear time for volumetric scatterers the typically regular distribution and shape of scattering elements in the inverse scattering problem allow the method to take advantage of data redundancy and reduce the computational demands of the normally expensive mlfma setup additional benefits are gained by employing kaczmarz like iterations where partial measurements are used to accelerate convergence numerical results demonstrate both the efficiency of the forward solver and the successful application of the inverse method to imaging problems with dimensions in the neighborhood of ten wavelengths

convergence of asynchronous distributed gradient methods over stochastic networks we consider distributed optimization problems in which a number of agents are to seek the global optimum of a sum of cost functions through only local information sharing in this paper we are particularly interested in scenarios where agents are operating asynchronously over stochastic networks subject to random failures most existing algorithms require coordinated and decaying stepsizes to ensure zero gap between the estimated value of each agent and the exact optimum restricting it from asynchronous implementation and resulting in slower convergence results to deal with this issue we develop a new asynchronous distributed gradient method asyndgm based on consensus theory the proposed algorithm not only allows for asynchronous implementation in a completely distributed manner but also most importantly is able to seek the exact optimum even with constant stepsizes we will show that the assumption of boundedness of gradients which is widely used in the literature can be dropped by instead imposing the standard lipschitz continuity condition on gradients moreover we derive an upper bound of stepsize within which the proposed asyndgm can achieve a linear convergence rate for strongly convex functions with lipschitz gradients a canonical example of sensor fusion problems is provided to illustrate the effectiveness of the proposed algorithm

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper