directional derivative of a minimax function etant donne une fonction a valeur reelle l definie sur x u v ou x est un espace localement convexe et ou u et v sont deux espaces topologiques de hausdorff on etudie l existence et la caracterisation de la derivee directionnelle dh x 0 d a x 0 x dans la direction d x de la fonction minimax h x sup v v o inf u u o l x u v ou u o et v o sont deux ensembles non vides dans u et dans v respectivement

a global algorithm for nonlinear semidefinite programming in this paper we propose a global algorithm for solving nonlinear semidefinite programming problems this algorithm inspired by the classic sqp sequentially quadratic programming method modifies the s sdp sequentially semidefinite programming local method by using a nondifferentiable merit function combined with a line search strategy

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

space frequency decomposition and time reversal imaging this paper presents two novel time reversal algorithms space frequency dort sf dort and sf multiple signal classification sf music to image targets based on the sf multistatic scattering data matrix singular value decomposition is applied to this matrix to obtain the left unitary matrix the vectors of which are classified into the signal subspace vectors corresponding to the targets and the noise subspace ones numerical simulations show that the imaging performances of the sf music and the sf dort are similar to those of the time reversal music tr music and the time domain dort td dort respectively however the new algorithms require only one single sf measurement by the tr array in contrast to n measurements needed in the tr music and the td dort when the tr array has n antennas

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

first and second order analysis of nonlinear semidefinite programs in this paper we study nonlinear semidefinite programming problems convexity duality and first order optimality conditions for such problems are presented a second order analysis is also given second order necessary and sufficient optimality conditions are derived finally sensitivity analysis of such programs is discussed

winner takes it all strongest node rule for evolution of scale free networks we study a model for evolution of complex networks we introduce information filtering for reduction of the number of available nodes to a randomly chosen sample as a stochastic component of evolution new nodes are attached to the nodes that have maximal degree in the sample this is a deterministic component of network evolution process this fact is unusual for evolution of scale free networks and depicts a possible route for modeling network growth we present both simulations and theoretical results for network evolution the obtained degree distributions exhibit an obvious power law behavior in the middle with the exponential cut off in the end this highlights the essential characteristics of information filtering in the network growth mechanisms

statistics for pulse reflection from a randomly layered medium we consider reflection of a pulse incident on a layered halfspace whose density and bulk modulus vary randomly we show that when the pulse width is long compared to the average time it takes to travel over one correlation length the reflected signal is approximately a gaussian random process the parameters of this process change slowly on a scale long compared to the pulse width we give a full characterization of the power spectrum of the gaussian process in terms of a universal function that does not depend on the medium

preferential attachment with information filtering node degree probability distribution properties abstract a network growth mechanism based on a two step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required in the first filtering step a subset of fixed size m of existing nodes is randomly chosen in the second step the preferential rule of attachment is applied to the chosen subset the characteristics of thus formed networks are explored using two approaches computer simulations of network growth and a theoretical description based on a master equation the results of the two approaches are in excellent agreement special emphasis is put on the investigation of the node degree probability distribution it is found that the tail of the distribution has the exponential form given by exp k m implications of the node degree distribution with such tail characteristics are briefly discussed

an analysis of new mixed finite elements for the approximation of wave propagation problems we construct and analyze a new family of rectangular two dimensional or cubic three dimensional mixed finite elements for the approximation of the acoustic wave equations the main advantage of this element is that it permits us to obtain through mass lumping an explicit scheme even in an anisotropic medium nonclassical error estimates are given for this new element

statistically stable ultrasonic imaging in random media analysis of array data from acoustic scattering in a random medium with a small number of isolated targets is performed in order to image and thereby localize the spatial position of each target because the host medium has random fluctuations in wave speed the background medium is itself a source of scattered energy it is assumed however that the targets are sufficiently larger and or more reflective than the background fluctuations so that a clear distinction can be made between targets and background scatterers in numerical simulations nonreflective boundary conditions are used so as to isolate the effects of the host randomness from those of the spatial boundaries which can then be treated in a separate analysis it is shown that the key to successful imaging is finding statistically stable functionals of the data whose extreme values provide estimates of scatterer locations the best ones are related to the eigenfunctions and eigenvalues of the array response matrix just as one might expect from prior work on array data processing in complex scattering media having homogeneous backgrounds the specific imaging functionals studied include matched field processing and linear subspace methods such as music mutiple signal classification but statistical stability is not characteristic of the frequency domain which is often the province of these methods by transforming back into the time domain after first diagonalizing the array data in the frequency domain one can take advantage of both the time domain stability and the frequency domain orthogonality of the relevant eigenfunctions

partially augmented lagrangian method for matrix inequality constraints we discuss a partially augmented lagrangian method for optimization programs with matrix inequality constraints a global convergence result is obtained applications to hard problems in feedback control are presented to validate the method numerically

robust control via sequential semidefinite programming this paper discusses nonlinear optimization techniques in robust control synthesis with special emphasis on design problems which may be cast as minimizing a linear objective function under linear matrix inequality lmi constraints in tandem with nonlinear matrix equality constraints the latter type of constraints renders the design numerically and algorithmically difficult we solve the optimization problem via sequential semidefinite programming ssdp a technique which expands on sequential quadratic programming sqp known in nonlinear optimization global and fast local convergence properties of ssdp are similar to those of sqp and ssdp is conveniently implemented with available semidefinite programming sdp solvers using two test examples we compare ssdp to the augmented lagrangian method another classical scheme in nonlinear optimization and to an approach using concave optimization

optimality conditions and global convergence for nonlinear semidefinite programming sequential optimality conditions have played a major role in unifying and extending global convergence results for several classes of algorithms for general nonlinear optimization in this paper we extend theses concepts for nonlinear semidefinite programming we define two sequential optimality conditions for nonlinear semidefinite programming the first is a natural extension of the so called approximate karush kuhn tucker akkt well known in nonlinear optimization the second one called trace akkt is more natural in the context of semidefinite programming as the computation of eigenvalues is avoided we propose an augmented lagrangian algorithm that generates these types of sequences and new constraint qualifications are proposed weaker than previously considered ones which are sufficient for the global convergence of the algorithm to a stationary point

second order optimality conditions based on parabolic second order tangent sets in this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints our analysis is based on various concepts of second order tangent sets and parametric duality we introduce a condition called second order regularity under which there is no gap between the corresponding second order necessary and second order sufficient conditions we show that the second order regularity condition always holds in the case of semidefinite programming

fast and efficient time reversal imaging using space frequency propagator method it is known that the eigenvalue decomposition and singular value decomposition svd of multi static data matrices mdms are the basis of time reversal tr imaging however the computational loads of the svd can be significantly high when the mdms are large the computational cost of the propagator method pm without any svd of mdms is much lower than that of svd based methods in this paper to reduce the computational complexity in tr imaging first a novel space frequency propagator method sf pm for tr imaging in large mdms is proposed the computational complexity of the proposed sf pm is then analyzed moreover the theoretical analysis is presented to show that the sf pm has a significantly lower computational complexity than the conventional svd based approach finally the reasonable imaging results and superior computational efficiency of the sf pm are verified by simulation

imaging of location and geometry for extended targets using the response matrix in this paper we study how to image both the location and the shape of extended targets using the response matrix obtained from inter element response of an active array of transducers in particular the time reversal technique is used for efficient initial localization of the target and the level set method is used for shape reconstruction we then show how to couple the location estimation and shape reconstruction in a complementary way to improve accuracy for range estimation resolution analysis for active arrays in remote sensing regime is also presented we illustrate with numerical experiments which show that the method is capable of imaging objects with complicated shapes and that the method is robust with respect to noisy data

analysis of the response matrix for an extended target in this paper we study the response matrix obtained from the interelement response of an active array of transducers that can send out signals and record reflected signals in particular we analyze the eigenvalues and eigenvectors of the response matrix corresponding to the acoustic field reflected by an extended target the size of which is comparable to the wavelength we show that the eigenvalues are not well separated for a single extended target in general however when both the size of the target and the size of the active array are small compared to the distance from the array to the target it is shown that the eigenvalues are well separated and that the leading eigenvalues and eigenvectors can be characterized in terms of the location and dimension of the target numerical experiments are presented to verify the analysis

on the sensitivity of time reversal imaging techniques to model perturbations time reversal tr techniques involve physical or synthetic retransmission of signals acquired by a set of transceivers in a time reversed fashion and can be used for a host of applications including ultrawideband imaging of obscured targets this work investigates the performance of some tr based techniques under non ideal conditions and is divided into three main parts in the first part we investigate the robustness of tr based imaging techniques via the decomposition of tr operator dort algorithm and the multiple signal classification music algorithm under clutter and additive noise in the second part we examine the effect of tr invariance breaking due to losses in the intervening media on the performance of both dort and tr based music in the third part effects of translational perturbations of the tr array are examined as a class of model perturbations these ensuing effects are then exploited in a controlled manner as a means to extract second order spatial statistics of the probed media

time reversal imaging for sensor networks with optimal compensation in time using extensive numerical simulations several distributed sensor imaging algorithms for localized damage in a structure are analyzed given a configuration of ultrasonic transducers a full response matrix for the healthy structure is assumed known it is used as a basis for comparison with the response matrix that is recorded when there is damage numerical simulations are done with the wave equation in two dimensions the healthy structure contains many scatterers the aim is to image point like defects with several regularly distributed sensors because of the complexity of the environment the recorded traces have a lot of delay spread and travel time migration does not work so well instead the traces are back propagated numerically assuming that there is some knowledge of the background since the time at which the back propagated field will focus on the defects is unknown the shannon entropy or the bounded variation norm of the image is computed and the time where it is minimal is picked this imaging method performs well because it produces a tight image near the location of the defects at the time of refocusing when there are several defects the singular value decomposition of the response matrix is also carried out

probing a random medium with a pulse this paper studies the reflection of pulses from a randomly layered half space it characterizes the statistical properties of the reflected signals at the surface in a suitable asymptotic limit in

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

an augmented lagrangian method for a class of lmi constrained problems in robust control theory we present a new approach to a class of non convex lmi constrained problems in robust control theory the problems we consider may be recast as the minimization of a linear objective subject to linear matrix inequality lmi constraints in tandem with non convex constraints related to rank deficiency conditions we solve these problems using an extension of the augmented lagrangian technique the lagrangian function combines a multiplier term and a penalty term governing the non convex constraints the lmi constraints due to their special structure are retained explicitly and not included in the lagrangian global and fast local convergence of our approach is then obtained either by an lmi constrained newton type method including line search or by a trust region strategy the method is conveniently implemented with available semi definite programming sdp interior point solvers we compare its performance to the wellknown d k iteration scheme in robust control two test problems are investigated and

decomposition of the time reversal operator detection and selective focusing on two scatterers the decomposition of the time reversal operator dort method is a selective detection and focusing technique using an array of transmit receive transducers it relies on the theory of iterative time reversal mirrors which was presented by prada et al c prada j l thomas and m fink j acoust soc am 97 62 71 1995 the time reversal operator was defined as k k where is the frequency means complex conjugate and k is the transfer matrix of the array of l transducers insonifying a time invariant scattering medium it was shown that this time reversal operator can be diagonalized and that for ideally resolved scatterers of different reflectivities each of its eigenvectors of nonzero eigenvalue provides the phase law to be applied to the transducers in order to focus on one of the scatterers the dort method consists in determining these eigenvectors and using them for the selective focusing this paper presents a complete analysis of this method in the case of two scatterers the

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved