optimal waveform selection for tracking systems investigates adaptive waveform selection schemes where selection is based on overall target tracking system performance optimal receiver assumptions allow the inclusion of transmitted waveform specification parameters in the tracking subsystem defining equations the authors give explicit expressions for two one step ahead optimization problems for a single target in white gaussian noise when the tracker is a conventional kalman filter these problems may be solved to yield the most improvement possible in tracking performance for each new transmitted pulse in cases where target motion is restricted to one dimension closed form solutions to the local one step ahead waveform optimization problem have been obtained the optimal waveform selection algorithms in the paper may be included with conventional kalman filtering equations to form an enhanced kalman tracker simulation examples are presented to illustrate the potential of the waveform selection schemes for the optimal utilization of the capabilities of modern digital waveform generators including multiple waveform classes the extension of the basic waveform optimization scheme to more complex tracking scenarios is also discussed

incremental stochastic subgradient algorithms for convex optimization this paper studies the effect of stochastic errors on two constrained incremental subgradient algorithms the incremental subgradient algorithms are viewed as decentralized network optimization algorithms as applied to minimize a sum of functions when each component function is known only to a particular agent of a distributed network first the standard cyclic incremental subgradient algorithm is studied in this the agents form a ring structure and pass the iterate in a cycle when there are stochastic errors in the subgradient evaluations sufficient conditions on the moments of the stochastic errors are obtained that guarantee almost sure convergence when a diminishing step size is used in addition almost sure bounds on the algorithm s performance with a constant step size are also obtained next the markov randomized incremental subgradient method is studied this is a noncyclic version of the incremental algorithm where the sequence of computing agents is modeled as a time nonhomogeneous markov chain such a model is appropriate for mobile networks as the network topology changes across time in these networks convergence results and error bounds for the markov randomized method in the presence of stochastic errors for diminishing and constant step sizes are obtained

adaptive high gain λ tracking with variable sampling rate it is well known that proportional output feedback control can stabilize any relative degree one minimum phase system if the sign of the feedback is correct and the proportional gain is high enough moreover there exists simple adaptation laws for tuning the proportional gain the so called high gain adaptive controllers which are not based on system identification or plant parameter estimation algorithms or injection of probing signals if tracking of signals is desired then these simple controllers are also applicable without invoking an internal model if the tracking error is not necessarily supposed to converge to zero but towards a ball around zero of arbitrarily small but prespecified radius 0 in this note we consider a sampled version of the high gain adaptive tracking controller the motivation for sampling arises from the possibility that the output of a system may not be available continuously but only at discrete time instants the problem is that the stiffness of the system increases as the proportional gain is increased our result shows that adaptive sampling tracking is possible if the product hk of the decreasing sampling rate h and the increasing proportional gain k decreases at a rate proportional to 1 logk

convergence of line search methods for unconstrained optimization line search methods are traditional and successful methods for solving unconstrained optimization problems its convergence has attracted more attention in recent years in this paper we analyze the general results on convergence of line search methods with seven line search rules it is clarified that the search direction plays a main role in these methods and that step size guarantees the global convergence in some cases it is also proved that many line search methods have same convergence property these convergence results can enable us to design powerful effective and stable algorithms in practice finally a class of special line search methods is investigated

adaptive sampled data tracking for input constrained exothermic chemical reaction models we consider digital input constrained adaptive and non adaptive output feedback control for a class of nonlinear systems which arise as models for controlled exothermic chemical reactors our objective is set point control of the temperature of the reaction with pre specifiedasymptotic tracking accuracy set by the designer our approach is basedon tracking controllers but in a context of piecewise constant sampled data output feedbacks and possibly adapted sampling periods the approach does not require any knowledge of the systems parameters does not invoke an internal model is simple in its design copes with noise corruptedoutput measurements andrequires only a feasibility assumption in terms of the reference temperature andthe input constraints

an optimal method for stochastic composite optimization this paper considers an important class of convex programming cp problems namely the stochastic composite optimization sco whose objective function is given by the summation of general nonsmooth and smooth stochastic components since sco covers non smooth smooth and stochastic cp as certain special cases a valid lower bound on the rate of convergence for solving these problems is known from the classic complexity theory of convex programming note however that the optimization algorithms that can achieve this lower bound had never been developed in this paper we show that the simple mirror descent stochastic approximation method exhibits the best known rate of convergence for solving these problems our major contribution is to introduce the accelerated stochastic approximation ac sa algorithm based on nesterov s optimal method for smooth cp nesterov in doklady an sssr 269 543 547 1983 nesterov in math program 103 127 152 2005 and show that the ac sa algorithm can achieve the aforementioned lower bound on the rate of convergence for sco to the best of our knowledge it is also the first universally optimal algorithm in the literature for solving non smooth smooth and stochastic cp problems we illustrate the significant advantages of the ac sa algorithm over existing methods in the context of solving a special but broad class of stochastic programming problems

convergence of approximate and incremental subgradient methods for convex optimization we present a unified convergence framework for approximate subgradient methods that covers various stepsize rules including both diminishing and nonvanishing stepsizes convergence in objective values and convergence to a neighborhood of the optimal set we discuss ways of ensuring the boundedness of the iterates and give efficiency estimates our results are extended to incremental subgradient methods for minimizing a sum of convex functions which have recently been shown to be promising for various large scale problems including those arising from lagrangian relaxation

brief paper an adaptive optimization scheme with satisfactory transient performance adaptive optimization ao schemes based on stochastic approximation principles such as the random directions kiefer wolfowitz rdkw the simultaneous perturbation stochastic approximation spsa and the adaptive fine tuning aft algorithms possess the serious disadvantage of not guaranteeing satisfactory transient behavior due to their requirement for using random or random like perturbations of the parameter vector the use of random or random like perturbations may lead to particularly large values of the objective function which may result to severe poor performance or stability problems when these methods are applied to closed loop controller optimization applications in this paper we introduce and analyze a new algorithm for alleviating this problem mathematical analysis establishes satisfactory transient performance and convergence of the proposed scheme under a general set of assumptions application of the proposed scheme to the adaptive optimization of a large scale complex control system demonstrates the efficiency of the proposed scheme

a policy gradient method for semi markov decision processes with application to call admission control solving a semi markov decision process smdp using value or policy iteration requires precise knowledge of the probabilistic model and suffers from the curse of dimensionality to overcome these limitations we present a reinforcement learning approach where one optimizes the smdp performance criterion with respect to a family of parameterised policies we propose an online algorithm that simultaneously estimates the gradient of the performance criterion and optimises it using stochastic approximation we apply our algorithm to call admission control our proposed policy gradient smdp algorithm and its application to admission control is novel

a new class of incremental gradient methods for least squares problems the least mean squares lms method for linear least squares problems differs from the steepest descent method in that it processes data blocks one by one with intermediate adjustment of the parameter vector under optimization this mode of operation often leads to faster convergence when far from the eventual limit and to slower sublinear convergence when close to the optimal solution we embed both lms and steepest descent as well as other intermediate methods within a one parameter class of algorithms and we propose a hybrid class of methods that combine the faster early convergence rate of lms with the faster ultimate linear convergence rate of steepest descent these methods are well suited for neural network training problems with large data sets furthermore these methods allow the effective use of scaling based for example on diagonal or other approximations of the hessian matrix

boundary conditions at fluid permeable interfaces in porous media a variational approach abstract a general set of boundary conditions at fluid permeable interfaces between dissimilar fluid filled porous matrices is established starting from an extended hamilton rayleigh principle these conditions do include friction and inertial effects once linearized they encompass boundary conditions relative to volume darcy brinkman and to surface saffman beavers joseph dissipation effects

general results on the convergence of stochastic algorithms a deterministic approach is proposed for proving the convergence of stochastic algorithms of the most general form under necessary conditions on the input noise and reasonable conditions on the nonnecessarily continuous mean field emphasis is placed on the case where more than one stationary point exists we also use this approach to prove the convergence of a stochastic algorithm with markovian dynamics

decentralized delay optimal control for interference networks with limited renewable energy storage in this paper we consider delay minimization for interference networks with renewable energy source where the transmission power of a node comes from both the conventional utility power ac power and the renewable energy source we assume the transmission power of each node is a function of the local channel state local data queue state and local energy queue state only we consider two delay optimization formulations namely the decentralized partially observable markov decision process dec pomdp and noncooperative partially observable stochastic game posg in dec pomdp formulation we derive a decentralized online learning algorithm to determine the control actions and lagrangian multipliers lms simultaneously based on the policy gradient approach under some mild technical conditions the proposed decentralized policy gradient algorithm converges almost surely to a local optimal solution in the noncooperative posg formulation the transmitter nodes are noncooperative we extend the decentralized policy gradient solution and establish the technical proof for almost sure convergence of the learning algorithms in both cases the solutions are very robust to model variations

particle filters for state estimation of jump markov linear systems jump markov linear systems jmls are linear systems whose parameters evolve with time according to a finite state markov chain in this paper our aim is to recursively compute optimal state estimates for this class of systems we present efficient simulation based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed lag smoothing problem our algorithms combine sequential importance sampling a selection scheme and markov chain monte carlo methods they use several variance reduction methods to make the most of the statistical structure of jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problems of on line deconvolution of impulsive processes and of tracking a maneuvering target are considered it is shown that our algorithms outperform the current methods

input constrained adaptive tracking with applications to exothermic chemical reaction models we consider input constrained adaptive output feedback control for a class of nonlinear systems which are prototype models for controlled exothermic chemical reactions our objective is set point control of the output i e the temperature of the reaction in the context of chemical reactions practical considerations lead us to work in the presence of input constraints we adopt an approach based on modified lambda tracking controllers whereby prespecified asymptotic tracking accuracy quantified by lambda 0 set by the designer is ensured the adaptive control strategy does not require any knowledge of the system s parameters and does not invoke an internal model only a feasibility assumption in terms of the reference temperature and the input constraints is assumed

power control with imperfect exchanges and applications to spectrum sharing in various applications the effect of errors in gradient based iterations is of particular importance when seeking saddle points of the lagrangian function associated with constrained convex optimization problems of particular interest here are problems arising in power control applications where network utility is maximized subject to minimum signal to interference plus noise ratio sinr constraints maximum interference constraints maximum received power constraints or simultaneous minimum and maximum sinr constraints especially when the gradient iterations are executed in a distributed fashion imperfect exchanges among the link nodes may result in erroneous gradient vectors in order to assess and cope with such errors two running averages ergodic sequences are formed from the iterates generated by the perturbed saddle point method each with complementary strengths under the assumptions of problem convexity and error boundedness bounds on the constraint violation and the suboptimality per iteration index are derived the two types of running averages are tested on a spectrum sharing problem with minimum and maximum sinr constraints as well as maximum interference constraints

global optimal feedback control for general nonlinear systems with nonquadratic performance criteria abstract optimal control of general nonlinear nonaffine controlled systems with nonquadratic performance criteria that permit state and control dependent time varying weighting parameters is solved classically using a sequence of linear quadratic and time varying problems the proposed method introduces an approximating sequence of riccati equations asre to explicitly construct nonlinear time varying optimal state feedback controllers for such nonlinear systems under very mild conditions of local lipschitz continuity the sequences converge globally to nonlinear optimal stabilizing feedback controls the computational simplicity and effectiveness of the asre algorithm is an appealing alternative to the tedious and laborious task of solving the hamilton jacobi bellman partial differential equation so the optimality of the asre control is studied by considering the original nonlinear nonquadratic optimization problem and the corresponding necessary conditions for optimality derived from pontryagin s maximum principle global optimal stabilizing state feedback control laws are then constructed this is compared with the optimality of the asre control by considering a nonlinear fighter aircraft control system which is nonaffine in the control numerical simulations are used to illustrate the application of the asre methodology which demonstrate its superior performance and optimality

linear stochastic approximation driven by slowly varying markov chains we study a linear stochastic approximation algorithm that arises in the context of reinforcement learning the algorithm employs a decreasing step size and is driven by markov noise with time varying statistics we show that under suitable conditions the algorithm can track the changes in the statistics of the markov noise as long as these changes are slower than the rate at which the step size of the algorithm goes to zero

efficient sequential monte carlo with multiple proposals and control variates sequential monte carlo is a useful simulation based method for online filtering of state space models for certain complex state space models a single proposal distribution is usually not satisfactory and using multiple proposal distributions is a general approach to address various aspects of the filtering problem this article proposes an efficient method of using multiple proposals in combination with control variates the likelihood approach of tan 2004 is used in both resampling and estimation the new algorithm is shown to be asymptotically more efficient than the direct use of multiple proposals and control variates the guidance for selecting multiple proposals and control variates is also given numerical examples are used to demonstrate that the new algorithm can significantly improve over the bootstrap filter and auxiliary particle filter

convergence property of gradient type methods with non monotone line search in the presence of perturbations in this paper two new kinds of methods which are called gradient type method and hybrid projection method with perturbations are proposed and non monotone line search technique is employed at the same time global convergence of these methods is proved only in the case where the gradient function is uniformly continuous on an open convex set containing the iteration sequence numerical examples are given at the end of this paper

gradient convergence in gradient methods with errors we consider the gradient method x t 1 x t g t s t w t where s t is a descent direction of a function f rn to re and w t is a deterministic or stochastic error we assume that gr f is lipschitz continuous that the stepsize g t diminishes to 0 and that s t and w t satisfy standard conditions we show that either f x t to infty or f x t converges to a finite value and gr f x t to0 with probability 1 in the stochastic case and in doing so we remove various boundedness conditions that are assumed in existing results such as boundedness from below of f boundedness of gr f x t or boundedness of xt

a simple selftuning controller for stably invertible systems in this paper we construct a new trajectory following adaptive control algorithm for linear time invariant finite dimensional systems that possess a stable inverse the exponential stability of the control scheme is demonstrated

optimal capacity allocation for sampled networked systems abstract we consider the problem of estimating the states of weakly coupled linear systems from sampled measurements we assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the estimation is bounded above and that each sample requires the same amount of communication our goal is then to find an optimal allocation of the capacity to the sensors so that the time averaged estimation error is minimized we show that when the total available channel capacity is large this resource allocation problem can be recast as a strictly convex optimization problem and hence there exists a unique optimal allocation of the capacity we further investigate how this optimal allocation varies as the available capacity increases in particular we show that if the coupling among the subsystems is weak then the sampling rate allocated to each sensor is nondecreasing in the total sampling rate and is strictly increasing if and only if the total sampling rate exceeds a certain threshold

on the convergence of the lms algorithm with adaptive learning rate for linear feedforward networks we consider the problem of training a linear feedforward neural network by using a gradient descent like lms learning algorithm the objective is to find a weight matrix for the network by repeatedly presenting to it a finite set of examples so that the sum of the squares of the errors is minimized kohonen showed that with a small but fixed learning rate or stepsize some subsequences of the weight matrices generated by the algorithm will converge to certain matrices close to the optimal weight matrix in this paper we show that by dynamically decreasing the learning rate during each training cycle the sequence of matrices generated by the algorithm will converge to the optimal weight matrix we also show that for any given 0 the lms algorithm with decreasing learning rates will generate an optimal weight matrix i e a matrix of distance at most away from the optimal matrix after o 1 training cycles this is in contrast to 1 log 1 training cycles needed to generate an optima

a stochastic successive minimization method for nonsmooth nonconvex optimization with applications to transceiver design in wireless communication networks consider the problem of minimizing the expected value of a cost function parameterized by a random variable the classical sample average approximation method for solving this problem requires minimization of an ensemble average of the objective at each step which can be expensive in this paper we propose a stochastic successive upper bound minimization method ssum which minimizes an approximate ensemble average at each iteration to ensure convergence and to facilitate computation we require the approximate ensemble average to be a locally tight upper bound of the expected cost function and be easily optimized the main contributions of this work include the development and analysis of the ssum method as well as its applications in linear transceiver design for wireless communication networks and online dictionary learning moreover using the ssum framework we extend the classical stochastic sub gradient method to the case of minimizing a nonsmooth nonconvex objective function and establish its convergence

a stochastic gradient type algorithm for closed loop problems we focus on the numerical solution of closed loop stochastic problems and propose a perturbed gradient algorithm to achieve this goal the main hurdle in such problems is the fact that the control variables are infinite dimensional due to e g the information constraints alternatively said control variables are feedbacks i e functions such controls have hence to be represented in a finite way in order to solve the problem numerically in the same way the gradient of the criterion is itself an infinite dimensional object our algorithm replaces this exact and unknown gradient by a perturbed one which consists of the product of the true gradient evaluated at a random point and a kernel function which extends this gradient to the neighbourhood of the random point proceeding this way we explore the whole space iteration after iteration through random points since each kernel function is perfectly known by a small number of parameters say n the control at iteration k is perfectly known as an infinite dimensional object by at most n k parameters the main strength of this method is that it avoids any discretization of the underlying space provided that we can sample as many points as needed in this space moreover our algorithm can take into account the possible measurability constraints of the problem in a new way finally the randomized strategy implemented by the algorithm causes the most probable parts of the space to be the most explored ones which is a priori an interesting feature in this paper we first prove two convergence results of this algorithm in the strongly convex and convex cases and then give some numerical examples showing the interest of this method for practical stochastic optimization problems

an online gradient based parameter identification algorithm for the neuro fuzzy systems abstract online gradient descent method has been widely applied for parameter learning in neuro fuzzy systems the success of the application relies on the convergence of the learning procedure however there barely have been convergence analyses on the online learning procedure for neuro fuzzy systems in this paper an online gradient learning algorithm with adaptive learning rate is proposed to identify the parameters of the neuro fuzzy systems representing the mamdani fuzzy model with gaussian fuzzy sets we take the reciprocals of the variances of the gaussian membership functions rather than the variances themselves as independent variables when computing the gradient with respect to the variance parameters subsequently oscillation of the gradient value in the learning process can be avoided furthermore some convergence results for this online learning scheme are studied finally three numerical examples are provided to illustrate the performance of the proposed algorithm

elastodynamics of an axisymmetric problem in an anisotropic liquid saturated porous medium the laplace and hankel transforms have been employed to find the general solution to the field equations in an anisotropic liquid saturated porous medium for plain axisymmetric problem in the transformed form an application of an infinite space with impulsive force at the origin has been considered to show the utility of the solution obtained the results of the corresponding problem in isotropic liquid saturated porous medium can be derived as a special case to get the solutions in the physical form a numerical inversion technique has been applied the results in the form of displacement and stress components have been obtained numerically and discussed graphically for a particular model

steered sequential projections for the inconsistent convex feasibility problem we study a steered sequential gradient algorithm which minimizes the sum of convex functions by proceeding cyclically in the directions of the negative gradients of the functions and using steered step sizes this algorithm is applied to the convex feasibility problem by minimizing a proximity function which measures the sum of the bregman distances to the members of the family of convex sets the resulting algorithm is a new steered sequential bregman projection method

characteristic analysis of wave propagation in anisotropic fluid saturated porous media in this investigation a characteristic analysis of stress wave propagation in anisotropic fluid saturated porous media is performed based on generalized characteristic theory this method enables us to carry out a complete basic analysis of wave propagation characteristic in fluid saturated porous media and immediately determine the wave fronts through the normal velocity surfaces first the characteristic differential equations and compatibility relations along bicharacteristics are deduced then the analytical expressions for the normal velocity surfaces and wave fronts are presented based on these equations the characteristic of the normal velocity surfaces and the wave fronts for all components of the stress waves in an orthotropic fluid saturated porous media as well as its special cases in three dimensional space is computed and discussed the results show that the wave fronts of fast and slow waves remain regular along with the increase of anisotropy of the media but great anisotropy may lead to more than one triple angle on the wave fronts of quasi transverse or transverse waves

input constrained funnel control with applications to chemical reactor models error feedback control in the presence of input constraints is considered for a class of exothermic chemical reactor models the primary control objective is regulation of a setpoint temperature t with prescribed accuracy given 0 arbitrarily small ensure that for every admissible system and reference setpoint the regulation error e t t is ultimately smaller than that is e t i for all t su4ciently large the second objective is guaranteed transient performance the evolution of the regulation error should be contained in a prescribed performance funnel f around the setpoint temperature t a simple error feedback control with input constraints of the form u t sat u 6 u k t t t t u u an o9set is introduced which achieves the objective in the presence of disturbances corrupting the measurement the gain k t is a function of the error e t t t t and its distance to the funnel boundary the input constraints u 6 u have to satisfy certain feasibility assumptions in terms of the model data and the operating point t

asynchronous stochastic approximations the asymptotic behavior of a distributed asynchronous stochastic approximation scheme is analyzed in terms of a limiting nonautonomous differential equation the relation between the latter and the relative values of suitably rescaled relative frequencies of updates of different components is underscored

posterior cramer rao bounds for discrete time nonlinear filtering a mean square error lower bound for the discrete time nonlinear filtering problem is derived based on the van trees 1968 posterior version of the cramer rao inequality this lower bound is applicable to multidimensional nonlinear possibly non gaussian dynamical systems and is more general than the previous bounds in the literature the case of singular conditional distribution of the one step ahead state vector given the present state is considered the bound is evaluated for three important examples the recursive estimation of slowly varying parameters of an autoregressive process tracking a slowly varying frequency of a single cisoid in noise and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation

a convergent incremental gradient method with a constant step size an incremental aggregated gradient method for minimizing a sum of continuously differentiable functions is presented the method requires a single gradient evaluation per iteration and uses a constant step size for the case that the gradient is bounded and lipschitz continuous we show that the method visits infinitely often regions in which the gradient is small under certain unimodality assumptions global convergence is established in the quadratic case a global linear rate of convergence is shown the method is applied to distributed optimization problems arising in wireless sensor networks and numerical experiments compare the new method with other incremental gradient methods

distributed optimization in an energy constrained network analog versus digital communication schemes we consider a distributed optimization problem whereby a network of n nodes sl l 1 n wishes to minimize a common strongly convex function f x x x1 xn t under the constraint that node sl controls variable xl only the nodes locally update their respective variables and periodically exchange their values with their neighbors over a set of predefined communication channels previous studies of this problem have focused mainly on the convergence issue and the analysis of convergence rate in this study we consider noisy communication channels and study the impact of communication energy on convergence in particular we study the minimum amount of communication energy required for nodes to obtain an e minimizer of f x in the mean square sense for linear analog communication schemes we prove that the communication energy to obtain an e minimizer of f x must grow at least at the rate of 1 e and this bound is tight when f is convex quadratic furthermore we show that the same energy requirement can be reduced to o log21 e if a suitable digital communication scheme is used

void probabilities and cauchy schwarz divergence for generalized labeled multi bernoulli models the generalized labeled multi bernoulli glmb is a family of tractable models that alleviates the limitations of the poisson family in dynamic bayesian inference of point processes in this paper we derive closed form expressions for the void probability functional and the cauchy schwarz divergence for glmbs the proposed analytic void probability functional is a necessary and sufficient statistic that uniquely characterizes a glmb while the proposed analytic cauchy schwarz divergence provides a tractable measure of similarity between glmbs we demonstrate the use of both results on a partially observed markov decision process for glmbs with cauchy schwarz divergence based reward and void probability constraint

a parallel decomposition method for nonconvex stochastic multi agent optimization problems this paper considers the problem of minimizing the expected value of a possibly nonconvex cost function parameterized by a random vector variable when the expectation cannot be computed accurately e g because the statistics of the random variables are unknown and or the computational complexity is prohibitive classical stochastic gradient methods for solving this problem may suffer from slow convergence in this paper we propose a stochastic parallel successive convex approximation based best response algorithm for general nonconvex stochastic sum utility optimization problems which arise naturally in the design of multi agent networks the proposed novel decomposition approach enables all users to update their optimization variables in parallel by solving a sequence of strongly convex subproblems one for each user almost sure convergence to stationary points is proved we then customize the algorithmic framework to solve the stochastic sum rate maximization problem over single input single output siso frequency selective interference channels multiple input multiple output mimo interference channels and mimo multiple access channels numerical results corroborate that the proposed algorithms can converge faster than state of the art stochastic gradient schemes while achieving the same or better sum rates

a distributed algorithm for convex constrained optimization under noise we present a novel distributed algorithm for convex constrained optimization problems that are subject to noise corruption and uncertainties the proposed scheme can be classified as a distributed stochastic approximation method where a unique feature here is that we allow for multiple noise terms to appear in both the computation and communication stages of the distributed iterative process specifically we consider problems that involve multiple agents optimizing a separable convex objective function subject to convex local constraints and linear coupling constraints this is a richer class of problems compared to those that can be handled by existing distributed stochastic approximation methods which consider only consensus constraints and fewer sources of noise the proposed algorithm utilizes the augmented lagrangian al framework which has been widely used recently to solve deterministic optimization problems in a distributed way we show that the proposed method generates sequences of primal and dual variables that converge to their respective optimal sets almost surely

on the equations governing the motion of an anisotropic poroelastic material we address biot s equations governing the motion of an anisotropic fluid saturated poroelastic material with certain properties first we investigate the uniqueness in solutions of the three dimensional governing equations for the regular region of the poroelastic material and enumerate the conditions sufficient for the uniqueness next by applying hamilton s principle to the motion of the region we obtain a variational principle that generates only the biot newton equations and the associated natural boundary conditions then by extending the variational principle for the region with an internal fixed surface of discontinuity through legendre s transformation we derive a six field variational principle that operates on all the poroelastic field variables the variational principle leads as its euler lagrange equations to all the governing equations including the jump conditions but the initial conditions as a generalized version of the hellinger reissner variational principle moreover we consider the free vibrations of the region and we discuss some basic properties of eigenvalues and present a variational formulation by rayleigh s quotient this work provides a standard tool with the features of variational principles when numerically solving the governing equations in heterogeneous media with finite element methods treating the free vibrations and consistently deriving some onedimensional two dimensional equations of the poroelastic region

sensor management for multi target tracking via multi bernoulli filtering abstract in multi object stochastic systems the issue of sensor management is a theoretically and computationally challenging problem in this paper we present a novel random finite set rfs approach to the multi target sensor management problem within the partially observed markov decision process pomdp framework the multi target state is modelled as a multi bernoulli rfs and the multi bernoulli filter is used in conjunction with two different control objectives maximizing the expected renyi divergence between the predicted and updated densities and minimizing the expected posterior cardinality variance numerical studies are presented in two scenarios where a mobile sensor tracks five moving targets with different levels of observability

the cauchy schwarz divergence for poisson point processes in this paper we extend the notion of cauchy schwarz divergence to point processes and establish that the cauchy schwarz divergence between the probability densities of two poisson point processes is half the squared l 2 distance between their intensity functions extension of this result to mixtures of poisson point processes and in the case where the intensity functions are gaussian mixtures closed form expressions for the cauchy schwarz divergence are presented our result also implies that the bhattacharyya distance between the probability distributions of two poisson point processes is equal to the square of the hellinger distance between their intensity measures we illustrate the result via a sensor management application where the system states are modeled as point processes

on stochastic gradient and subgradient methods with adaptive steplength sequences traditionally stochastic approximation sa schemes have been popular choices for solving stochastic optimization problems however the performance of standard sa implementations can vary significantly based on the choice of the steplength sequence and in general little guidance is provided about good choices motivated by this gap we present two adaptive steplength schemes for strongly convex differentiable stochastic optimization problems equipped with convergence theory that aim to overcome some of the reliance on user specific parameters the first scheme referred to as a recursive steplength stochastic approximation rsa scheme optimizes the error bounds to derive a rule that expresses the steplength at a given iteration as a simple function of the steplength at the previous iteration and certain problem parameters the second scheme termed as a cascading steplength stochastic approximation csa scheme maintains the steplength sequence as a piecewise constant decreasing function with the reduction in the steplength occurring when a suitable error threshold is met then we allow for nondifferentiable objectives but with bounded subgradients over a certain domain in such a regime we propose a local smoothing technique based on random local perturbations of the objective function that leads to a differentiable approximation of the function assuming a uniform distribution on the local randomness we establish a lipschitzian property for the gradient of the approximation and prove that the obtained lipschitz bound grows at a modest rate with problem size this facilitates the development of an adaptive steplength stochastic approximation framework which now requires sampling in the product space of the original measure and the artificially introduced distribution

dgm a deep learning algorithm for solving partial differential equations abstract high dimensional pdes have been a longstanding computational challenge we propose to solve high dimensional pdes by approximating the solution with a deep neural network which is trained to satisfy the differential operator initial condition and boundary conditions our algorithm is meshfree which is key since meshes become infeasible in higher dimensions instead of forming a mesh the neural network is trained on batches of randomly sampled time and space points the algorithm is tested on a class of high dimensional free boundary pdes which we are able to accurately solve in up to 200 dimensions the algorithm is also tested on a high dimensional hamilton jacobi bellman pde and burgers equation the deep learning algorithm approximates the general solution to the burgers equation for a continuum of different boundary conditions and physical conditions which can be viewed as a high dimensional space we call the algorithm a deep galerkin method dgm since it is similar in spirit to galerkin methods with the solution approximated by a neural network instead of a linear combination of basis functions in addition we prove a theorem regarding the approximation power of neural networks for a class of quasilinear parabolic pdes

robust inversion dimensionality reduction and randomized sampling we consider a class of inverse problems in which the forward model is the solution operator to linear odes or pdes this class admits several dimensionality reduction techniques based on data averaging or sampling which are especially useful for large scale problems we survey these approaches and their connection to stochastic optimization the data averaging approach is only viable however for a least squares misfit which is sensitive to outliers in the data and artifacts unexplained by the forward model this motivates us to propose a robust formulation based on the student s t distribution of the error we demonstrate how the corresponding penalty function together with the sampling approach can obtain good results for a large scale seismic inverse problem with 50 corrupted data

simulation based optimal sensor scheduling with application to observer trajectory planning the sensor scheduling problem can be formulated as a controlled hidden markov model and this paper solves the problem when the state observation and action spaces are continuous this general case is important as it is the natural framework for many applications the aim is to minimise the variance of the estimation error of the hidden state w r t the action sequence we present a novel simulation based method that uses a stochastic gradient algorithm to find optimal actions

incremental proximal methods for large scale convex optimization we consider the minimization of a sum sum i 1 mf i x consisting of a large number of convex component functions f i for this problem incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective we propose new incremental methods consisting of proximal iterations applied to single components as well as combinations of gradient subgradient and proximal iterations we provide a convergence and rate of convergence analysis of a variety of such methods including some that involve randomization in the selection of components we also discuss applications in a few contexts including signal processing and inference machine learning

from structured data to evolution linear partial differential equations abstract this paper is devoted to the derivation of computational methods for constructing partial differential equations from data following some recent works 7 14 15 20 we propose a methodology based on symbolic calculus 8 9 13 pseudospectral methods 2 3 and stochastic processes 6 in order to determine non constant coefficients of linear evolution partial differential equations pdes from a set of structured data constituted by solutions at given times and positions of an unknown linear pde

the optimal observability of partially observable markov decision processes discrete state space we consider autonomous partially observable markov decision processes where the control action influences the observation process only considering entropy as the cost incurred by the markov information state process the optimal observability problem is posed as a markov decision scheduling problem that minimizes the infinite horizon cost this scheduling problem is shown to be equivalent to minimization of an entropy measure called estimation entropy which is related to the invariant measure of the information state

dynamic behaviour of an anisotropic liquid saturated porous medium in frequency domain a general solution to the field equations of an anisotropic liquid saturated porous medium has been obtained in the transformed form using the fourier transform assuming the disturbances to be harmonically time dependent the transformed solution is obtained in the frequency domain an application of a time harmonic concentrated force acting at some interior point of an infinite medium has been considered to show the utility of the solution obtained the transformed solutions are inverted numerically using a numerical inversion technique to invert the fourier transform the results in the form of stress components have been obtained numerically and discussed graphically for a particular model the results of the corresponding problem in isotropic liquid saturated porous medium can be derived as a special case