fundamental limitations in passive time delay estimation part i narrow band systems time delay estimation of a noise like random signal observed at two or more spatially separated receivers is a problem of considerable practical interest in passive radar sonar applications a new method is presented to analyze the mean square error performance of delay estimation schemes based on a modified improved version of the ziv zakai lower bound zzlb this technique is shown to yield the tightest results on the attainable system performance for a wide range of signal to noise ratio snr conditions for delay estimation using narrow band ambiguity prone signals the fundamental result of this study is illustrated in fig 3 the entire domain of snr is divided into several disjoint segments indicating several distinct modes of operation if the available snr does not exceed snr 1 signal observations from the receiver outputs are completely dominated by noise thus essentially useless for the delay estimation as a result the attainable mean square error bar epsilon 2 is bounded only by the a priori parameter domain if snr 1 2 the modified zzlb coincides with the barankin bound in this regime differential delay observations are subject to ambiguities if snr snr 3 the modified zzlb coincides with the cramer rao lower bound indicating that the ambiguity in the differential delay estimation can essentially be resolved the transition from the ambiguity dominated mode of operation to the ambiguity free mode of operation starts at snr 2 and ends at snr 3 this is the threshold phenomenon in time delay estimation the various deflection points snr i and the various segments of the bound fig 3 are given as functions of such important system parameters as time bandwidth product wt signal bandwidth to center frequency ratio w 0 and the number of half wavelengths of the signal center frequency contained in the spacing between receivers with this information the composite bound illustrated in fig 3 provides the most complete characterization of the attainable system performance under any prespecified snr conditions

confidence regions for stochastic variational inequalities the sample average approximation saa method is a basic approach for solving stochastic variational inequalities svi it is well known that under appropriate conditions the saa solutions provide asymptotically consistent point estimators for the true solution to an svi it is of fundamental interest to use such point estimators along with suitable central limit results to develop confidence regions of prescribed level of significance for the true solution however standard procedures are not applicable because the central limit theorem that governs the asymptotic behavior of saa solutions involves a discontinuous function evaluated at the true solution of the svi this paper overcomes such a difficulty by exploiting the precise geometric structure of the variational inequalities and by appealing to certain large deviations probability estimates and proposes a method to build asymptotically exact confidence regions for the true solution that are computable from the saa solutions we justify this method theoretically by establishing a precise limit theorem apply it to complementarity problems and test it with a linear complementarity problem

primal dual interior point methods for semidefinite programming convergence rates stability and numerical results primal dual interior point path following methods for semidefinite programming are considered several variants are discussed based on newton s method applied to three equations primal feasibility dual feasibility and some form of centering condition the focus is on three such algorithms called the xz xz zx and q methods for the xz zx and q algorithms the newton system is well defined and its jacobian is nonsingular at the solution under nondegeneracy assumptions the associated schur complement matrix has an unbounded condition number on the central path under the nondegeneracy assumptions and an additional rank assumption practical aspects are discussed including mehrotra predictor corrector variants and issues of numerical stability compared to the other methods considered the xz zx method is more robust with respect to its ability to step close to the boundary converges more rapidly and achieves higher accuracy

quantitative stability analysis of stochastic quasi variational inequality problems and applications we consider a parametric stochastic quasi variational inequality problem sqvip for short where the underlying normal cone is defined over the solution set of a parametric stochastic cone system we investigate the impact of variation of the probability measure and the parameter on the solution of the sqvip by reformulating the sqvip as a natural equation and treating the orthogonal projection over the solution set of the parametric stochastic cone system as an optimization problem we effectively convert stability of the sqvip into that of a one stage stochastic program with stochastic cone constraints under some moderate conditions we derive holder outer semicontinuity and continuity of the solution set against the variation of the probability measure and the parameter the stability results are applied to a mathematical program with stochastic semidefinite constraints and a mathematical program with sqvip constraints

characterization of the robust isolated calmness for a class of conic programming problems this paper is devoted to studying the robust isolated calmness of the karush kuhn tucker kkt solution mapping for a large class of interesting conic programming problems including most commonly known ones arising from applications at a locally optimal solution under the robinson constraint qualification we show that the kkt solution mapping is robustly isolated calm if and only if both the strict robinson constraint qualification and the second order sufficient condition hold this implies among others that at a locally optimal solution the second order sufficient condition is needed for the kkt solution mapping to have the aubin property

on the r superlinear convergence of the kkt residuals generated by the augmented lagrangian method for convex composite conic programming due to the possible lack of primal dual type error bounds it was not clear whether the karush kuhn tucker kkt residuals of the sequence generated by the augmented lagrangian method alm for solving convex composite conic programming cccp problems converge superlinearly in this paper we resolve this issue by establishing the r superlinear convergence of the kkt residuals generated by the alm under only a mild quadratic growth condition on the dual of cccp with easy to implement stopping criteria for the augmented lagrangian subproblems this discovery may help to explain the good numerical performance of several recently developed semismooth newton cg based alm solvers for linear and convex quadratic semidefinite programming

the q stirling numbers continued fractions and the q charlier and q laguerre polynomials we give a simple proof of the continued fraction expansions of the ordinary generating functions of the q stirling numbers of both kinds by generalizing the method of touchard 1956 and milne 1978 we obtain the explicit formulas and measure of one set of the polynomials whose moments are the q stirling numbers

the direct extension of admm for multi block convex minimization problems is not necessarily convergent the alternating direction method of multipliers admm is now widely used in many fields and its convergence was proved when two blocks of variables are alternatively updated it is strongly desirable and practically valuable to extend the admm directly to the case of a multi block convex minimization problem where its objective function is the sum of more than two separable convex functions however the convergence of this extension has been missing for a long time neither an affirmative convergence proof nor an example showing its divergence is known in the literature in this paper we give a negative answer to this long standing open question the direct extension of admm is not necessarily convergent we present a sufficient condition to ensure the convergence of the direct extension of admm and give an example to show its divergence

bayesian bounds for matched field parameter estimation matched field methods concern estimation of source locations and or ocean environmental parameters by exploiting full wave modeling of acoustic waveguide propagation because of the nonlinear parameter dependence of the signal field the estimate is subject to ambiguities and the sidelobe contribution often dominates the estimation error below a threshold signal to noise ratio snr to study the matched field performance three bayesian lower bounds on mean square error are developed the bayesian crame spl acute r rao bound bcrb the weiss weinstein bound wwb and the ziv zakai bound zzb particularly for a multiple frequency multiple snapshot random signal model a closed form minimum probability of error associated with the likelihood ratio test is derived which facilitates error analysis in a wide scope of applications analysis and example simulations demonstrate that 1 unlike the local crb the bcrb is not achieved by the maximum likelihood estimate mle even at high snr if the local performance is not uniform across the prior parameter space 2 the zzb gives the closest mle performance prediction at most snr levels of practical interest 3 the zzb can also be used to determine the necessary number of independent snapshots achieving the asymptotic performance of the mle at a given snr 4 incoherent frequency averaging which is a popular multitone processing approach reduces the peak sidelobe error but may not improve the overall performance due to the increased ambiguity baseline and finally 5 effects of adding additional parameters e g environmental uncertainty can be well predicted from the parameter coupling

stochastic variational inequalities residual minimization smoothing sample average approximations the stochastic variational inequality vi has been used widely in engineering and economics as an effective mathematical model for a number of equilibrium problems involving uncertain data this paper presents a new expected residual minimization erm formulation for a class of stochastic vi the objective of the erm formulation is lipschitz continuous and semismooth which helps us guarantee the existence of a solution and convergence of approximation methods we propose a globally convergent a s smoothing sample average approximation ssaa method to minimize the residual function this minimization problem is convex for the linear stochastic vi if the expected matrix is positive semidefinite we show that the erm problem and its ssaa problems have minimizers in a compact set and any cluster point of minimizers and stationary points of the ssaa problems is a minimizer and a stationary point of the erm problem a s our examples come from applications involving traffic flow problems we show that t

on the combinatorics of normal ordering bosonic operators and deformations of it recently some combinatorial aspects for the normal ordering of powers of arbitrary monomials of boson operators were discussed in particular it was shown that the resulting formulae lead to generalizations of the usual bell and stirling numbers in this paper these considerations are generalized to the q deformed case in particular it is shown that the simplest example of this generalization leads to q deformed lah numbers the connection between generalized stirling and bell numbers and matrix elements of the above mentioned operators with respect to the usual fock space basis and coherent states is discussed

general second order covariance of gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides a method is provided for determining necessary conditions on sample size or signal to noise ratio snr to obtain accurate parameter estimates from remote sensing measurements in fluctuating environments these conditions are derived by expanding the bias and covariance of maximum likelihood estimates mles in inverse orders of sample size or snr where the first order covariance term is the cramer rao lower bound crlb necessary sample sizes or snrs are determined by requiring that i the first order bias and the second order covariance are much smaller than the true parameter value and the crlb respectively and ii the crlb falls within desired error thresholds an analytical expression is provided for the second order covariance of mles obtained from general complex gaussian data vectors which can be used in many practical problems since i data distributions can often be assumed to be gaussian by virtue of the central limit theorem and ii it allows for both the mean and variance of the mea

the derivative of a waveguide acoustic field with respect to a three dimensional sound speed perturbation semianalytic expressions are derived for the first order derivative of a pressure field in a laterally homogeneous waveguide with respect to an arbitrary three dimensional refractive index perturbation in either the water column or ocean bottom these expressions for the environmental derivative derived using an adjoint method require a three dimensional spatial correlation between two green s functions weighted by an environmental parameter basis function with the green s functions expressed in terms of normal modes when a particular set of orthogonal spatial basis functions is chosen the three dimensional spatial integral can be converted into a set of one dimensional integrations over depth and azimuth the use of the orthogonal basis permits environmental derivatives to be computed for an arbitrary sound speed perturbation to illustrate the formulas a simple sensitivity study is presented that explores under what circumstances three dimensional plane wave and cylindrical perturbations produ

a new inexact alternating directions method for monotone variational inequalities the alternating directions method adm is an effective method for solving a class of variational inequalities vi when the proximal and penalty parameters in sub vi problems are properly selected in this paper we propose a new adm method which needs to solve two strongly monotone sub vi problems in each iteration approximately and allows the parameters to vary from iteration to iteration the convergence of the proposed adm method is proved under quite mild assumptions and flexible parameter conditions

a queueing model and a set of orthogonal polynomials a single serving queueing model is studied where potential customers are discouraged at the rate n qn 0 q 1 n is the queue length the serving rate is n 1 qn n 0 1 the spectral function is computed and the corresponding set of orthogonal polynomials is studied in detail the slightly more general model with n qn 1 bqn n 1 qn 1 bqn and the analogous orthogonal polynomials are also investigated in both cases a method developed by pollaczek is used which has been used very successfully to study new sets of orthogonal polynomials by askey and ismail

quantitative stability analysis for minimax distributionally robust risk optimization this paper considers distributionally robust formulations of a two stage stochastic programming problem with the objective of minimizing a distortion risk of the minimal cost incurred at the second stage we carry out a stability analysis by looking into variations of the ambiguity set under the wasserstein metric decision spaces at both stages and the support set of the random variables in the case when the risk measure is risk neutral the stability result is presented with the variation of the ambiguity set being measured by generic metrics of zeta structure which provides a unified framework for quantitative stability analysis under various metrics including total variation metric and kantorovich metric when the ambiguity set is structured by a zeta ball we find that the hausdorff distance between two zeta balls is bounded by the distance of their centers and difference of their radii the findings allow us to strengthen some recent convergence results on distributionally robust optimization where the center of the wasserstein ball is constructed by the empirical probability distribution

convergence analysis for mathematical programs with distributionally robust chance constraint convergence analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and the optimal solutions and research on this topic has been well documented in the literature of stochastic programming in this paper we extend such analysis to optimization problems with distributionally robust chance constraints where the true probability distribution is unknown but it is possible to construct an ambiguity set of probability distributions and the chance constraint is based on the most conservative selection of probability distribution from the ambiguity set the convergence analysis focuses on impact of the variation of the ambiguity set on the optimal value and the optimal solutions we start by deriving general convergence results under abstract conditions such as continuity of the robust probability function and uniform convergence of the robust probability functions and followed with detailed analysis of these

an efficient inexact symmetric gauss seidel based majorized admm for high dimensional convex composite conic programming in this paper we propose an inexact multi block admm type first order method for solving a class of high dimensional convex composite conic optimization problems to moderate accuracy the design of this method combines an inexact 2 block majorized semi proximal admm and the recent advances in the inexact symmetric gauss seidel sgs technique for solving a multi block convex composite quadratic programming whose objective contains a nonsmooth term involving only the first block variable one distinctive feature of our proposed method the sgs imspadmm is that it only needs one cycle of an inexact sgs method instead of an unknown number of cycles to solve each of the subproblems involved with some simple and implementable error tolerance criteria the cost for solving the subproblems can be greatly reduced and many steps in the forward sweep of each sgs cycle can often be skipped which further contributes to the efficiency of the proposed method global convergence as well as the iteration complexity in the non ergodic sense is established preliminary numerical experiments on some high dimensional linear and convex quadratic sdp problems with a large number of linear equality and inequality constraints are also provided the results show that for the vast majority of the tested problems the sgs imspadmm is 2 3 times faster than the directly extended multi block admm with the aggressive step length of 1 618 which is currently the benchmark among first order methods for solving multi block linear and quadratic sdp problems though its convergence is not guaranteed

some polynomials related to dowling lattices and x stieltjes moment sequences abstract in this paper we first introduce two sequences of polynomials which unify many well known polynomials related to dowling lattices including the bell polynomials and the dowling polynomials then we show the x stieltjes moment property of these polynomial sequences by their continued fractions and a criterion based on sokal wang and zhu independently

a note on upper lipschitz stability error bounds and critical multipliers for lipschitz continuous kkt systems we prove a new local upper lipschitz stability result and the associated local error bound for solutions of parametric karush kuhn tucker systems corresponding to variational problems with lipschitzian base mappings and constraints possessing lipschitzian derivatives and without any constraint qualifications this property is equivalent to the appropriately extended to this nonsmooth setting notion of noncriticality of the lagrange multiplier associated to the primal solution which is weaker than second order sufficiency all this extends several results previously known only for optimization problems with twice differentiable data or assuming some constraint qualifications in addition our results are obtained in the more general variational setting

local duality of nonlinear programs it is shown that the second order sufficient necessary optimality condition for the dual of a nonlinear program is equivalent to the inverse of the hessian of the lagrangian being positive definite semidefinite on the normal cone to the local primal constraint surface this compares with the hessian itself being positive definite semidefinite on the tangent cone on the local primal constraint surface for the corresponding second order condition for the primal problem we also show that primal second order sufficiency necessity and dual second order necessity sufficiency is essentially equivalent to the hessian of the lagrangian being positive definite this follows from the following interesting linear algebra result a necessary and sufficient condition for a nonsingular symmetric n times n matrix to be positive definite is that for some subspace of r n the matrix must be positive definite on the subspace and its inverse be positive semidefinite on the orthogonal complement of the subspace

necessary conditions for a maximum likelihood estimate to become asymptotically unbiased and attain the cramer rao lower bound ii range and depth localization of a sound source in an ocean waveguide analytic expressions for the first order bias and second order covariance of a maximum likelihood estimate mle are applied to the problem of localizing an acoustic source in range and depth in a shallow water waveguide with a vertical hydrophone array these expressions are then used to determine necessary conditions on sample size or equivalently signal to noise ratio snr for the localization mle to become asymptotically unbiased and attain minimum variance as expressed by the cramer rao lower bound crlb these analytic expressions can be applied in a similar fashion to any ocean acoustic inverse problem involving random data both deterministic and completely randomized signals embedded in independent and additive waveguide noise are investigated as the energy ratio of received signal to additive noise sanr descends to the lower operational range of a typical passive localization system source range and depth estimates exhibit significant biases and have variances that can exceed the crlb by orders of magnitude the spatial structure of the bias suggests that acoustic range and depth estimates tend to converge around particular range and depth cells for moderate sanr values

asymptotic theory for solutions in statistical estimation and stochastic programming new techniques of local sensitivity analysis for nonsmooth generalized equations are applied to the study of sequences of statistical estimates and empirical approximations to solutions of stochastic programs consistency is shown to follow from a certain local invertibility property and asymptotic distributions are derived from a generalized implicit function theorem that characterizes asymptotic behavior in situations where estimates are subjected to constraints and estimation functionals are nonsmooth

linear rate convergence of the alternating direction method of multipliers for convex composite programming in this paper we aim to prove the linear rate convergence of the alternating direction method of multipliers admm for solving linearly constrained convex composite optimization problems under a mild calmness condition which holds automatically for convex composite piecewise linear quadratic programming we establish the global q linear rate of convergence for a general semi proximal admm with the dual step length being taken in 0 1 51 2 2 this semi proximal admm which covers the classic one has the advantage to resolve the potentially nonsolvability issue of the subproblems in the classic admm and possesses the abilities of handling the multi block cases efficiently we demonstrate the usefulness of the obtained results when applied to two and multi block convex quadratic semidefinite programming

restricted growth functions rank row matchings of partition lattices and q stirling numbers abstract in this paper we use restricted growth functions to give a direct algebraic description of the incidence relations of the lattice of partitions of an n set that is independent of the partitions themselves this description of the incidence relations not only gives new information about rank row matchings of partition lattices but is of independent interest since every finite lattice is a sublattice of some partition lattice as a further application of restricted growth functions we show how the polynomials in q known as q stirling numbers of the second kind may be viewed as generating functions

sensitivity analysis for cone constrained optimization problems under the relaxed constraint qualifications we present the local sensitivity analysis for cone constrained optimization problems under the cq type conditions significantly weaker than those traditionally used in this context our basic sensitivity results are established under the first or second order sufficient optimality conditions combined with the estimate of the distance to the feasible set of the perturbed problem we demonstrate how such an estimate can be obtained under the assumptions weaker than robinson s cq and establish the corresponding sensitivity results finally we apply our results to sensitivity analysis and relaxation schemes for mathematical programs with complementarity constraints

local linear convergence of the alternating direction method of multipliers on quadratic or linear programs we introduce a novel matrix recurrence yielding a new spectral analysis of the local transient convergence behavior of the alternating direction method of multipliers admm for the particular case of a quadratic program or a linear program we identify a particular combination of vector iterates whose convergence can be analyzed via a spectral analysis the theory predicts that admm should go through up to four convergence regimes such as constant step convergence or linear convergence ending with the latter when close enough to the optimal solution if the optimal solution is unique and satisfies strict complementarity

quantitative stability analysis for distributionally robust optimization with moment constraints in this paper we consider a broad class of distributionally robust optimization dro problems where the probability of the underlying random variables depends on the decision variables and the ambiguity set is defined through parametric moment conditions with generic cone constraints under some moderate conditions including slater type conditions of a cone constrained moment system and holder continuity of the underlying random functions in the objective and moment conditions we show local holder continuity of the optimal value function of the inner maximization problem with respect to w r t the decision vector and other parameters in moment conditions and local holder continuity of the optimal value of the whole minimax dro w r t the parameter moreover under the second order growth condition of the lagrange dual of the inner maximization problem we demonstrate and quantify the outer semicontinuity of the set of optimal solutions of the minimax dro w r t variation of the parameter finally w

a convergent 3 block semiproximal alternating direction method of multipliers for conic programming with 4 type constraints in this paper we consider conic programming problems whose constraints consist of linear equalities linear inequalities a nonpolyhedral cone and a polyhedral cone a convenient way for solving this class of problems is to apply the directly extended alternating direction method of multipliers admm to its dual problem which has been observed to perform well in numerical computations but may diverge in theory ideally one should find a convergent variant which is at least as efficient as the directly extended admm in practice we achieve this goal by designing a convergent semiproximal admm called spadmm3c for convenience for convex programming problems having three separable blocks in the objective function with the third part being linear at each iteration the proposed spadmm3c takes one special block coordinate descent bcd cycle with the order 1 rightarrow 3 rightarrow 2 rightarrow 3 instead of the usual 1 rightarrow 2 rightarrow 3 gauss seidel bcd cycle used in the nonconvergent directly extended 3 block admm for updating the variable blocks our numerical experiments demonstrate that the convergent method is at least 20 faster than the directly extended admm with unit step length for the vast majority of about 550 large scale doubly nonnegative semidefinite programming problems with linear equality and or inequality constraints this confirms that at least for conic convex programming one can design a convergent and efficient admm with a special bcd cycle of updating the variable blocks

quantitative stability analysis of stochastic generalized equations we consider the solution of a system of stochastic generalized equations sge where the underlying functions are mathematical expectation of random set valued mappings sge has many applications such as characterizing optimality conditions of a nonsmooth stochastic optimization problem or equilibrium conditions of a stochastic equilibrium problem we derive quantitative continuity of expected value of the set valued mapping with respect to the variation of the underlying probability measure in a metric space this leads to the subsequent qualitative and quantitative stability analysis of solution set mappings of the sge under some metric regularity conditions we derive aubin s property of the solution set mapping with respect to the change of probability measure the established results are applied to stability analysis of stochastic variational inequality stationary points of classical one stage and two stage stochastic minimization problems two stage stochastic mathematical programs with equilibriu

sensitivity analysis of parameterized variational inequalities in this paper we discuss local uniqueness continuity and differentiability properties of solutions of parameterized variational inequalities generalized equations to this end we use two types of techniques one approach consists in formulating variational inequalities in a form of optimization problem based on regularized gap functions and applying a general theory of perturbation analysis of parameterized optimization problems another approach is based on a theory of contingent outer graphical derivatives and some results about differentiability properties of metric projections

second order variational analysis in second order cone programming the paper conducts a second order variational analysis for an important class of nonpolyhedral conic programs generated by the so called second order lorentz ice cream cone mathcal q from one hand we prove that the indicator function of mathcal q is always twice epi differentiable and apply this result to characterizing the uniqueness of lagrange multipliers together with an error bound estimate in the general second order cone programming setting involving twice differentiable data on the other hand we precisely calculate the graphical derivative of the normal cone mapping to mathcal q under the metric subregularity constraint qualification and then give an application of the latter result to a complete characterization of isolated calmness for perturbed variational systems associated with second order cone programs the obtained results seem to be the first in the literature in these directions for nonpolyhedral problems without imposing any nondegeneracy assumptions

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

on the linearization problem involving pochhammer symbols and their q analogues abstract in this paper we present a simple recurrent algorithm for solving the linearization problem involving some families of q polynomials in the exponential lattice x s c1qs c3 some simple examples are worked out in detail

recurrence relations for connection coefficients between q orthogonal polynomials of discrete variables in the non uniform lattice x s q2s we obtain the structure relations for q orthogonal polynomials in the exponential lattice and from these we construct the recurrence relation for the connection coefficients between two families of polynomials belonging to the classical class of discrete q orthogonal polynomials an explicit example is also given

quantitative stability of two stage distributionally robust risk optimization problem with full random linear semi definite recourse abstract in this paper we study a distributionally robust risk optimization drro problem where the information on the probability distribution of the underlying random variables is incomplete but it is possible to use partial information to construct an ambiguity set of probability distributions in some cases decision vector x may have a direct impact on the likelihood of the underlying random events that occur after the decision is taken which motivates us to propose an ambiguity set to be parametric and decision dependent to conduct quantitative stability analysis of the optimal value function and the optimal solution mapping of the drro problem we derive error bounds results for the parametrized ambiguity set under the total variation metric and investigate lipschitz continuity of the objective function of the drro problem under some conditions as an application we demonstrate that the two stage stochastic linear semi definite programs satisfy these conditions and then apply results obtained to it

necessary conditions for a maximum likelihood estimate to become asymptotically unbiased and attain the cramer rao lower bound part i general approach with an application to time delay and doppler shift estimation analytic expressions for the first order bias and second order covariance of a general maximum likelihood estimate mle are presented these expressions are used to determine general analytic conditions on sample size or signal to noise ratio snr that are necessary for a mle to become asymptotically unbiased and attain minimum variance as expressed by the cramer rao lower bound crlb the expressions are then evaluated for multivariate gaussian data the results can be used to determine asymptotic biases variances and conditions for estimator optimality in a wide range of inverse problems encountered in ocean acoustics and many other disciplines the results are then applied to rigorously determine conditions on snr necessary for the mle to become unbiased and attain minimum variance in the classical active sonar and radar time delay and doppler shift estimation problems the time delay mle is the time lag at the peak value of a matched filter output it is shown that the matched filter estimate a

resolving lambertian surface orientation from fluctuating radiance a maximum likelihood method for estimating remote surface orientation from multi static acoustic optical radar or laser images is presented it is assumed that the images are corrupted by signal dependent noise known as speckle arising from complex gaussian field fluctuations and that the surface properties are effectively lambertian surface orientation estimates for a single sample are shown to have biases and errors that vary dramatically depending on illumination direction this is due to the signal dependent nature of speckle noise and the nonlinear relationship between surface orientation illumination direction and fluctuating radiance the minimum number of independent samples necessary for maximum likelihood estimates to become asymptotically unbiased and to attain the lower bound on resolution of classical estimation theory are derived as are practical design thresholds

normal ordering for nonlinear deformed ladder operators and the f generalization of the stirling and bell numbers we resolve the normal ordering problem for symmetric d d n and asymmetric d rd n strings of the nonlinear deformed ladder operators d for supersymmetric and shape invariant potential systems where r and n are positive integers we provide exact and explicit expressions for their normal forms n d d n and n d rd n where in n all d are at the right side we find that the solutions involve sequence of expansion coefficients which for r n 1 corresponds to the f deformed generalization of the classical stirling and bell numbers of the second kind we apply the general formalism for the translational shape invariant potential systems as well as for the particular case of the harmonic oscillator potential system we show that these numbers are obtained for families of polynomial expressions generated with the deformations parameters and the parameters related to the forms of the supersymmetric partner potentials

stability analysis of two stage stochastic mathematical programs with complementarity constraints via nlp regularization this paper presents numerical approximation schemes for a two stage stochastic programming problem where the second stage problem has a general nonlinear complementarity constraint first the complementarity constraint is approximated by a parameterized system of inequalities with a well known regularization approach by scholtes siam j optim 11 2001 pp 918 936 in deterministic mathematical programs with equilibrium constraints the distribution of the random variables of the regularized two stage stochastic program is then approximated by a sequence of probability measures by treating the approximation problems as a perturbation of the original true problem we carry out a detailed stability analysis of the approximated problems including continuity and local lipschitz continuity of optimal value functions and outer semicontinuity and continuity of the set of optimal solutions and stationary points a particular focus is given to the case where the probability distribution is approximated by

asymptotic accuracy of geoacoustic inversions criteria necessary to accurately estimate a set of unknown geoacoustic parameters from remote acoustic measurements are developed in order to aid the design of geoacoustic experiments the approach is to have estimation error fall within a specified design threshold by adjusting controllable quantities such as experimental sample size or signal to noise ratio snr this is done by computing conditions on sample size and snr necessary for any estimate to have a variance that 1 asymptotically attains the cramer rao lower bound crlb and 2 has a crlb that falls within the specified design error threshold applications to narrow band deterministic signals received with additive noise by vertical and horizontal arrays in typical continental shelf waveguides are explored for typical low frequency scenarios necessary snrs and samples sizes can often approach prohibitively large values when a few or more important geoacoustic parameters are unknown making it difficult to attain practical design threshold

improved local convergence results for augmented lagrangian methods in varvec c mathbf 2 c2 cone reducible constrained optimization this paper deals with a class of cone reducible constrained optimization problems which encompasses nonlinear programming semidefinite programming second order cone programming and any combination thereof using the second order sufficient condition and a strict version of the robinson constraint qualification we provide a semi local error bound which generalizes known results from the literature moreover under the same assumptions we prove that an augmented lagrangian method is locally convergent with rate proportional to 1 rho k where rho k is the penalty parameter and that rho k remains bounded