penalty functions in e programming and e minimax problems several authors have been intersted in optimality conditions in e programming and in e minimas problem see for example the references 11 16

equivalence between two dimensional analytic and real signal wigner distributions a solution to the problem of undesired cross terms in the wigner distribution wd of two dimensional real signals is presented the solution is to introduce the notion of two dimensional analytic signal in the wd the relation between wds of the two dimensional real signal and those of its associated two dimensional analytical signal is discussed and illustrated by an example

efficient computation of the discrete pseudo wigner distribution a description is given of a novel algorithm the fast fourier transform in part fftp for the computation of the discrete pseudo wigner distribution dpwd the fftp computes the cosine and sine parts of the discrete fourier transform dft separately by employing real inverse sinusoidal twiddle factors unlike the conventional methods which directly utilize the complex dft the fftp yields real output since the dpwd is always real in addition the new method reduces the computational cost by making full use of symmetries and removing redundancies in the fftp computation the authors also describe a simple algorithm for computing the discrete hilbert transform dht to produce the nonaliased dpwd a pipeline structure for real time and a bulk processing technique for offline implementations of the method are presented

wigner distribution of noisy signals the effect of noise on the wigner distribution is analyzed the mean and variance of the wigner distribution of signals contaminated by additive noise are derived it is shown that in the case of white noise the wigner distribution calculated by definition calculated by definition cannot be used for estimation for estimation windowing in the time domain is not sufficient smoothing in the time domain is necessary very simple expressions for variance and bias estimation are obtained if the signal and noise are analytic only one window is sufficient to make the variance finite the results are demonstrated by numerical examples with linear and sinusoidal chirp pulses

e optimality and duality for multiobjective fractional programming abstract using the scalar e parametric approach we establish the karush kuhn tucker which we call kkt necessary and sufficient conditions for an e pareto optimum of nondifferentiable multiobjective fractional objective functions subject to nondifferentiable convex inequality constraints linear equality constraints and abstract constraints these optimality criteria are utilized as a basis for constructing one duality model with appropriate duality theorems subsequently we employ scalar exact penalty function to transform the multiobjective fractional programming problem to an unconstrained problem under this case we derive the kkt necessary and sufficient conditions without a constraint qualification for e pareto optimality of multiobjective fractional programming

wigner ville spectral analysis of nonstationary processes the wigner ville spectrum has been recently introduced as the unique generalized spectrum for time varying spectral analysis its properties are revised with emphasis on its central role in the analysis of second order properties of nonstationary random signals we propose here a general class of spectral estimators of the wigner ville spectrum this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the general class of conjoint time frequency representations of deterministic signals with finite energy classical estimators like short time periodograms and the recently introduced pseudo wigner estimators are shown to be special cases of the general class the generalized framework allows the calculation of the moments of general spectral estimators and comparing the results emphasizes the versatility of the new pseudo wigner estimators the effective numerical implementation by an n point fft of pseudo wigner estimators of 2n points is indicated and various examples are given

accurate bidiagonal decomposition of totally positive cauchy vandermonde matrices and applications abstract cauchy vandermonde matrices play a fundamental role in rational interpolation theory and in other fields when all their corresponding nodes are different and positive and all poles are different and negative and follow adequate orderings these matrices are totally positive in this paper we provide fast algorithms for computing bidiagonal factorizations of these matrices and their inverses with high relative accuracy these algorithms can be used to solve with high relative accuracy other algebraic problems such as the computation of all singular values all eigenvalues or the solution of certain linear systems the error analysis of the algorithm for computing the bidiagonal factorization and the corresponding perturbation theory are also performed

epsilon approximate solutions for multiobjective programming problems abstract in this paper approximate solutions for multiobjective programming problems up to 0 are investigated the concepts of approximate solutions were introduced by white and loridan the connections with these concepts are studied also the sufficient and necessary conditions to obtain the elements of the smallest approximate solution set are verified

accurate computations with collocation matrices of rational bases the rational bernstein basis plays a crucial role in computer aided geometric design the collocation matrices of this basis are called rational bernstein vandermonde matrices in this paper we provide algorithms for computing the bidiagonal decomposition of rational bernstein vandermonde matrices and their inverses with high relative accuracy similar results are obtained for the collocation matrices of another important rational basis the rational said ball basis it is also shown that these algorithms can be used to perform accurately some computations with these matrices such us the calculation of their inverses their eigenvalues or their singular values numerical experiments illustrate the results

on the wigner distribution of discrete time noisy signals with application to the study of quantization effects the influence of noise on the wigner distribution wd of discrete time signals is analyzed signals contaminated by white noise are considered the expressions for the mean and variance of the wd estimator are derived it is then shown that the application of only one window is sufficient to make the variance of the estimator finite this is a significant difference from the analog case where two windows are needed the expression for the optimal window width is derived the results are illustrated by several numerical examples using the derived expressions the effects of finite register length on the wd are analyzed fixed and floating point arithmetic are considered

accurate bidiagonal decomposition of totally positive h bernstein vandermonde matrices and applications abstract an algorithm for the computation of the bidiagonal decomposition of strictly totally positive h bernstein vandermonde matrices is presented these matrices are collocation matrices of h bernstein bases a generalization of the bernstein basis of the space of polynomials of degree less than or equal to n the algorithm is fast its computational complexity is o n 2 and has high relative accuracy the computation of this bidiagonal decomposition is used as the initial stage for the accurate and efficient solution of several linear algebra problems with these matrices linear system solving eigenvalue computation and inverse computation numerical experiments are also included

ϵ pareto optimality for nondifferentiable multiobjective programming via penalty function abstract necessary and sufficient conditions without a constraint qualification for pareto optimality of multiobjective programming are derived the necessary kuhn tucker condition suggests the establishment of a wolf type duality theorem for nondifferentiable convex multiobjective minimization problems the generalized saddle point for pareto optimality of the vector lagrangian is studied

composite nonsmooth multiobjective programs with v ρ invexity abstract in this paper some problems consisting of nonsmooth composite multiobjective programs have been treated with v invexity type of conditions in particular we prove the generalized karush kuhn tucker sufficient optimality theorem and duality theorems for nonsmooth composite multiobjective programs also weak vector saddle point theorems are obtained for the composite programs under v invexity conditions the results obtained generalize the results of hun kuk et al to some extent

generating epsilon efficient solutions in multiobjective programming scalarization approaches to purposely generating e efficient solutions of multiobjective programs are investigated and a generic procedure for computing these solutions is proposed and illustrated with an example real life decision making situations in which the solutions are of significance are described

e optimality for multiobjective programming on a banach space abstract we establish a lagrange multiplier rule in terms of clarke generalized gradient that characterizes e efficiency of a nondifferentiable multiobjective programming problem on a real banach space this rule is then utilized to establish relationship between e efficient solution of multiobjective program and generalized saddle point of an appropriate vector valued lagrangian under invexity hypothesis

a unified definition for the discrete time discrete frequency and discrete time frequency wigner distributions various discrete definitions of the wigner distribution wd for discrete time signals have been proposed in previous works the formulation developed in this paper leads to natural and unified definitions of discrete versions of the wd they are directly related to the continuous and preserve most of its properties the discretization is first considered in the time domain dtwd in the frequency domain dfwd and then in both domains simultaneously dtfwd in each case the aliasing problem is studied and generalized interpolation formulas allowing the reconstruction of the continuous wd are derived the dtfwd is particulary relevant for computer implementation of the wd

accurate computations with said ball vandermonde matrices abstract a generalization of the vandermonde matrices which arise when the power basis is replaced by the said ball basis is considered when the nodes are inside the interval 0 1 then those matrices are strictly totally positive an algorithm for computing the bidiagonal decomposition of those said ball vandermonde matrices is presented which allows us to use known algorithms for totally positive matrices represented by their bidiagonal decomposition the algorithm is shown to be fast and to guarantee high relative accuracy some numerical experiments which illustrate the good behaviour of the algorithm are included

parametric approaches to fractional programs the fractional program p is defined by maxf x g x subject tox x a class of methods for solving p is based on the auxiliary problem q with a parameter maxf x g x subject tox x starting with two classical methods in this class the newton method and the binary search method a number of variations are introduced and compared among the proposed methods the modified binary search method is theoretically interesting because of its superlinear convergence and the capability to provide an explicit interval containing the optimum parameter value bar lambda computational behavior is tested by solving fractional knapsack problems and quadratic fractional programs the interpolated binary search method seems to be most efficient while other methods also behave surprisingly well

total positivity and neville elimination abstract neville elimination is described in terms of schur complements of matrices and used to improve some well known characterizations of totally positive and strictly totally positive matrices

a chain rule for ɛ subdifferentials with applications to approximate solutions in convex pareto problems abstract in this work we obtain a chain rule for the approximate subdifferential considering a vector valued proper convex function and its post composition with a proper convex function of several variables nondecreasing in the sense of the pareto order we derive an interesting formula for the conjugate of a composition in the same framework and we prove the chain rule using this formula to get the results we require qualification conditions since in the composition the initial function is extended vector valued this chain rule extends analogous well known calculus rules obtained when the functions involved are finite and it gives a complementary simple expression for other chain rules proved without assuming any qualification condition as application we deduce the well known calculus rule for the addition and we extend the formula for the maximum of functions finally we use them and a scalarization process to obtain kuhn tucker type necessary and sufficient conditions for approximate solutions in convex pareto problems these conditions extend other obtained in scalar optimization problems

accurate svds of polynomial vandermonde matrices involving orthonormal polynomials abstract we present a new o n3 algorithm for computing the svd of an n n polynomial vandermonde matrix vp pi 1 xj to high relative accuracy in o n3 time the pi are orthonormal polynomials deg pi i and xj are complex nodes the small singular values of vp can be arbitrarily smaller than the largest ones so that traditional algorithms typically compute them with no relative accuracy at all we show that the singular values even the tiniest ones are usually well conditioned functions of the data xj justifying this computation we also explain how this theory can be extended to other polynomial vandermonde matrices involving polynomials that are not orthonormal or even orthogonal

positive time frequency distribution functions we demonstrate the existence of positive joint distributions of time and frequency for arbitrary signals a method is given to readily generate an infinite number of them for any signal general properties of these distribution functions are derived and specific examples for some common signals are presented

the aliasing problem in discrete time wigner distributions there is no straightforward way to proceed from the continuous time wigner distribution to a discrete time version of this time frequency signal representation a previously given definition of such a function turned out to yield a distribution that was periodic with period instead of 2 and this caused aliasing to occur various alternative definitions are considered and compared with respect to aliasing and computational complexity from this comparison it appears that no definition leads to a function that is optimum in all respects this is illustrated by an example

the wigner distribution of noisy signals with adaptive time frequency varying window time frequency representations using the wigner distribution wd may be significantly obscured by the noise in the observations the analysis performed for the wd of discrete time noisy signals shows that this time frequency representation can be optimized by the appropriate choice of the window length however the practical value of this analysis is not significant because the optimization requires knowledge of the bias which depends on the unknown derivatives of the wd a simple adaptive algorithm for the efficient time frequency representation of noisy signals is developed in this paper the algorithm uses only the noisy estimate of the wd and the analytical formula for the variance of this estimate the quality of this adaptive algorithm is close to the one that could be achieved by the algorithm with the optimal window length provided that the wd derivatives were known in advance the proposed algorithm is based on the idea that has been developed in our previous work for the instantaneous frequency if estimation here a direct addressing to the wd itself rather than to the instantaneous frequency resulted in a time and frequency varying window length and showed that the assumption of small noise and bias is no longer necessary a simplified version of the algorithm using only two different window lengths is presented it is shown that the procedure developed for the adaptive window length selection can be generalized for application on multicomponent signals with any distribution from the cohen 1989 1990 1992 class simulations show that the developed algorithms are efficient even for a very low value of the signal to noise ratio

ϵ optimality criteria for vector minimization problems via exact penalty functions abstract several authors have been interested in optimality criteria for scalar programming problems in this paper some optimality results for the scalar problems of ours math programming 56 1992 233 243 are extended to vector minimization problems via exact penalty functions similar to our paper the solvability of neither the vector problems nor the associated dual problems is assumed our criteria are derived by estimating the size of the penalty parameter in terms of approximate solutions for the dual problems

an analysis of instantaneous frequency representation using time frequency distributions generalized wigner distribution this paper presents an analysis of the representation of instantaneous frequency using time frequency distributions of energy density domain similarity to the ideal instantaneous frequency presentation is chosen as a criterion for comparison of various distributions although all the commonly used distributions suffer from the artifacts along frequency axis it is shown that the wigner distribution is the best among them with respect to this criterion the generalization of wigner distribution lwd is introduced to decrease the artifacts the properties of the lwd are analyzed it is shown that at the expense of an insignificant increase in computation time much better results are obtained the theory is illustrated by a numerical example with the frequency modulated signals

time varying filtering and signal estimation using wigner distribution synthesis techniques the short time fourier transform stft the ambiguity function af and the wigner distribution wd are mixed time frequency signal representations that use fourier transform techniques to map a one dimensional function of time into a two dimensional function of time and frequency these mixed time frequency mappings have been used to analyze the local frequency characteristics of a variety of signals and systems although much work has also been done to develop stft and af synthesis algorithms that can be used to implement a variety of time varying signal processing operations no such synthesis techniques have thus far been developed for the wd in this paper a signal synthesis algorithm that works directly with the real valued high resolution wd will be derived examples of how this wd synthesis procedure can be used to perform time varying filtering operations or signal separation will be given

e optimality criteria for convex programming problems via exact penalty functions in this paper we presente optimality criteria for convex programming problems associated with exact penalty functions several authors have given various criteria under the assumption that such convex problems and the associated dual problems can be solved we assume the solvability of neither the convex problem nor the dual problem to derive our criteria we estimate the size of the penalty parameter in terms of ane solution for the dual problem

accurate computation of the moore penrose inverse of strictly totally positive matrices abstract the computation of the moore penrose inverse of structured strictly totally positive matrices is addressed since these matrices are usually very ill conditioned standard algorithms fail to provide accurate results an algorithm based on the q r factorization and which takes advantage of the special structure and the totally positive character of these matrices is presented the first stage of the algorithm consists of the accurate computation of the bidiagonal decomposition of the matrix numerical experiments illustrating the good behavior of our approach are included

a dual differentiable exact penalty function a new penalty function is associated with an inequality constrained nonlinear programming problem via its dual this penalty function is globally differentiable if the functions defining the original problem are twice globally differentiable in addition the penalty parameter remains finite this approach reduces the original problem to a simple problem of maximizing a globally differentiable function on the product space of a euclidean space and the nonnegative orthant of another euclidean space many efficient algorithms exist for solving this problem for the case of quadratic programming the penalty function problem can be solved effectively by successive overrelaxation sor methods which can handle huge problems while preserving sparsity features

e optimal solutions in nondifferentiable convex programming and some related questions in this paper we present e optimality conditions of the kuhn tucker type for points which are within e of being optimal to the problem of minimizing a nondifferentiable convex objective function subject to nondifferentiable convex inequality constraints linear equality constraints and abstract constraints such e optimality conditions are of interest for theoretical consideration as well as from the computational point of view some illustrative applications are made thus we derive an expression for the e subdifferential of a general convex max function we also show how the e optimality conditions given in this paper can be mechanized into a bundle algorithm for solving nondifferentiable convex programming problems with linear inequality constraints

a matricial description of neville elimination with applications to total positivity abstract the neville elimination process used by the authors in some previous papers in connection with totally positive matrices is studied in detail in the case of nonsingular matrices a wide class of matrices is found where neville elimination has a lower computational cost than gauss elimination finally some new characterizations are obtained for strictly totally positive and nonsingular totally positive matrices in terms of their neville elimination and that of their inverses

sufficiency of exact penalty minimization by employing a recently obtained error bound for differentiable convex inequalities it is shown that under appropriate constraint qualifications a minimum solution of an exact penalty function for a single value of the penalty parameter which exceeds a certain threshold is also a solution of the convex program associated with the penalty function no a priori assumption is made regarding the solvability of the convex program if such a solvability assumption is made then we show that a threshold value of the penalty parameter can be used which is smaller than both the above mentioned value and that of zangwill these various threshold values of the penalty parameter also apply to the well known big m method of linear programming

a method for time frequency analysis a method for time frequency signal analysis is presented the proposed method belongs to the general class of smoothed pseudo wigner distributions it is derived from the analysis of the wigner distribution defined in the frequency domain this method provides some substantial advantages over the wigner distribution the well known cross term effects are reduced or completely removed the oversampling of signal is not necessary in addition the computation time can be significantly shorter the results are demonstrated on two numerical examples with frequency modulated signals

minimum variance time frequency distribution kernels when dealing with random processes reduced spectrum estimate variance becomes an important property that augments the list of desirable time frequency t f distribution properties in this correspondence we derive the t f kernel that satisfies the t f constraints and provides the minimum variance for the power spectrum estimate for gaussian white noise processes

bidiagonal decomposition of rectangular totally positive said ball vandermonde matrices error analysis perturbation theory and applications abstract an algorithm for computing the bidiagonal decomposition of said ball vandermonde matrices in the rectangular case is presented which allows one to use known algorithms for totally positive matrices represented by their bidiagonal decomposition the algorithm is fast and possesses high relative accuracy the error analysis of the algorithm is also addressed along with the perturbation theory for the bidiagonal factorization of totally positive said ball vandermonde matrices some numerical experiments showing the good behavior of the algorithm are included