construction of robust frames in erasure recovery abstract erasures occur often in signal transmission in 10 the authors introduced robust frames with which one can recover erased frame coefficients even if the locations are unknown in this paper we give some explicit construction of robust frames

burst erasures and the mean square error for cyclic parseval frames this paper investigates the performance of frames for the linear redundant encoding of vectors when consecutive frame coefficients are lost due to the occurrence of random burst errors we assume that the distribution of bursts is invariant under cyclic shifts and that the burst length statistics are known in analogy with rate distortion theory we wish to find frames of a given size which minimize the mean square reconstruction error for the encoding of vectors in a complex finite dimensional hilbert space we obtain an upper bound for the mean square reconstruction error for a given parseval frame and in the case of cyclic parseval frames we find a family of frames which minimizes this upper bound under certain conditions these minimizers are identical to complex bose chaudhuri hocquenghem codes discussed in the literature the accuracy of our upper bounds for the mean square error is substantiated by complementary lower bounds all estimates are based on convexity arguments and a discrete rearrangement inequality

a stochastic estimation algorithm with observation averaging an algorithm for the constrained problem of estimating the regression coefficients is presented the algorithm is based on the idea of direct averaging of the observations in order to estimate the search direction it is shown that if the true parameter belongs to the permitted set then the algorithm delivers asymptotically optimal estimates of the parameter finite convergence of the method is proved when the true parameter lies outside the permitted set

robust h filtering for nonlinear systems abstract a robust or h approach to filtering for nonlinear systems is considered a bound on the estimate error as a function of the disturbance energy is obtained the corresponding dynamic programming equation is a first order pde this has computational ramifications the case where the measurements are discrete time is considered also a numerical method is discussed

hybrid filtering for linear systems with non gaussian disturbances this paper is concerned with hybrid filtering of a non gaussian system coupled by a hidden switching process an optimal control approach is used to derive a finite dimensional recursive filter that is optimal in the sense of the most probable trajectory mpt estimate an approximate scheme is obtained when the probability distribution of the switching process converges to a limiting distribution which is often easier to obtain numerical examples are considered and computational experiments are reported in these examples our schemes outperform popular filtering schemes available in the literature

a lagrangian based heuristic for large scale set covering problems we present a new lagrangian based heuristic for solving large scale set covering problems arising from crew scheduling at the italian railways ferrovie dello stato our heuristic obtained impressive results when compared to state of the art codes on a test bed provided by the company which includes instances with sizes ranging from 50 000 variables and 500 constraints to 1 000 000 variables and 5000 constraints 1998 the mathematical programming society inc published by elsevier science b v

frames graphs and erasures two uniform frames and their use for the coding of vectors are the main subject of this paper these frames are known to be optimal for handling up to two erasures in the sense that they minimize the largest possible error when up to two frame coefficients are set to zero here we consider various numerical measures for the reconstruction error associated with a frame when an arbitrary number of the frame coefficients of a vector are lost we derive general error bounds for two uniform frames when more than two erasures occur and apply these to concrete examples we show that among the 227 known equivalence classes of two uniform 36 15 frames arising from hadamard matrices there are 5 that give smallest error bounds for up to 8 erasures

optimal frames for erasures we study frames from the viewpoint of coding theory we introduce a numerical measure of how well a frame reconstructs vectors when some of the frame coefficients of a vector are lost and then attempt to find and classify the frames that are optimal in this setting

linearly connected sequences and spectrally optimal dual frames for erasures abstract in the case that a frame is prescribed for applications and erasures occur in the process of data transmissions we examine optimal dual frames for the recovery from single erasures in contrast to earlier papers we consider the spectral radius of the error operator instead of its operator norm as a measure of optimality this notion of optimality is natural when the neumann series is used to recover the original data in an iterative manner we obtain a complete characterization of spectrally one erasure optimal dual frames in terms of the redundancy distribution of the prescribed frame our characterization relies on the connection between erasure optimal frames and the linear connectivity property of the frame we prove that the linear connectivity property is equivalent to the intersection dependent property and is also closely related to the well known concept of a k independent set additionally we also establish several necessary and sufficient conditions for the existence of an alternate dual frame to make the iterative reconstruction work

variable metric bundle methods from conceptual to implementable forms to minimize a convex function we combine moreau yosida regularizations quasi newton matrices and bundling mechanisms first we develop conceptual forms using reversal quasi newton formulae and we state their global and local convergence then to produce implementable versions we incorporate a bundle strategy together with a curve search no convergence results are given for the implementable versions however some numerical illustrations show their good behaviour even for large scale problems

linear regression and filtering under nonstandard assumptions arbitrary noise this note is devoted to parameter estimation in linear regression and filtering where the observation noise does not possess any nice probabilistic properties in particular the noise might have an unknown but bounded deterministic nature the basic assumption is that the model regressors inputs are random optimal rates of convergence for the modified stochastic approximation and least squares algorithms are established under some weak assumptions typical behavior of the algorithms in the presence of such deterministic noise is illustrated by numerical examples

lagrangean heuristics for location problems abstract in this paper we present a framework for developing lagrangean heuristics heuristics based upon lagrangean relaxation and subgradient optimisation with respect to location problems computational results are given for four different location problems p median uncapacitated warehouse location capacitated warehouse location and capacitated warehouse location with single source constraints these results indicate that the framework presented in this paper is robust i e it gives good quality solutions for each of these different location problems

presolving in linear programming most modern linear programming solvers analyze the lp problem before submitting it to optimization some examples are the solvers whizard tomlin and welch 1983 ob1 lustig et al 1994 osl forrest and tomlin 1992 sciconic 1990 and cplex bixby 1994 the purpose of the presolve phase is to reduce the problem size and to discover whether the problem is unbounded or infeasible in this paper we present a comprehensive survey of presolve methods moreover we discuss the restoration procedure in detail i e the procedure that undoes the presolve computational results on the netlib problems gay 1985 are reported to illustrate the efficiency of the presolve methods

necessary and sufficient conditions for stability of lms guo and ljung 1995 established some general results on exponential stability of random linear equations which can be applied directly to the performance analysis of a wide class of adaptive algorithms including the basic lms ones without requiring stationarity independency and boundedness assumptions of the system signals the current paper attempts to give a complete characterization of the exponential stability of the lms algorithms by providing a necessary and sufficient condition for such a stability in the case of possibly unbounded nonstationary and non spl phi mixing signals the results of this paper can be applied to a very large class of signals including those generated from e g a gaussian process via a time varying linear filter as an application several novel and extended results on convergence and the tracking performance of lms are derived under various assumptions neither stationarity nor markov chain assumptions are necessarily required in the paper

computational study of large scale p median problems given a directed graph g v a the p median problem consists of determining p nodes the median nodes minimizing the total distance from the other nodes of the graph we present a branch and cut and price algorithm yielding provably good solutions for instances with v 3795 key ingredients of the algorithm are a delayed column and row generation technique exploiting the special structure of the formulation to solve the lp relaxation and cutting planes to strengthen the formulation and limit the size of the enumeration tree

equiangular tight frames from complex seidel matrices containing cube roots of unity we derive easily verifiable conditions which characterize when complex seidel matrices containing cube roots of unity have exactly two eigenvalues the existence of such matrices is equivalent to the existence of equiangular tight frames for which the inner product between any two frame vectors is always a common multiple of the cube roots of unity we also exhibit a relationship between these equiangular tight frames complex seidel matrices and highly regular directed graphs we construct examples of such frames with arbitrarily many vectors

optimally sparse frames frames have established themselves as a means to derive redundant yet stable decompositions of a signal for analysis or transmission while also promoting sparse expansions however when the signal dimension is large the computation of the frame measurements of a signal typically requires a large number of additions and multiplications and this makes a frame decomposition intractable in applications with limited computing budget to address this problem in this paper we focus on frames in finite dimensional hilbert spaces and introduce sparsity for such frames as a new paradigm in our terminology a sparse frame is a frame whose elements have a sparse representation in an orthonormal basis thereby enabling low complexity frame decompositions to introduce a precise meaning of optimality we take the sum of the numbers of vectors needed from this orthonormal basis when expanding each frame vector as sparsity measure we then analyze the recently introduced algorithm spectral tetris for construction of unit norm tight frames and prove that the tight frames generated by this algorithm are in fact optimally sparse with respect to the standard unit vector basis finally we show that even the generalization of spectral tetris for the construction of unit norm frames associated with a given frame operator produces optimally sparse frames

reconstruction of signals from frame coefficients with erasures at unknown locations we propose new approaches to the problems of recovering signals from the rearranged frame coefficients or frame coefficients with erasures at either known or unknown locations these problems naturally arise from applications where the encoded information needs to be transmitted for example in signal image processing information and coding theory and communications we show that with the appropriate choices of the frames that are used for encoding the signal with erasures occurring at known locations can be easily recovered without inverting the sub frame operators each time our new easy to implement and cost efficient algorithm provides perfect reconstruction of the original signal to address the problem of recovering erased coefficients from unknown locations we propose to use a class of frames that are almost robust with respect to m erasures we prove that every frame with uniform excess can be rescaled to an almost robust frame and the locations of erased data can be perfectly recovered for almost all the signals similar results are obtained for recovering the original order of a disordered rearranged set of frame coefficients numerical examples are presented to test the main results whenever the received data are noise free we can recover the original signal exactly from frame coefficients with erasures at unknown locations or from a disordered set of frame coefficients

convergence analysis of adaptive linear estimation for dependent stationary processes the convergence properties of an adaptive linear mean square estimator that uses a modified lms algorithm are established for generally dependent processes bounds on the mean square error of the estimates of the filter coefficients and on the excess error of the estimate of the signal are derived for input processes which are either strong mixing or asymptotically uncorrelated it is shown that the mean square deviation is bounded by a constant multiple of the adaptation step size and that the same holds for the excess error of the signal estimation the present findings extend earlier results in the literature obtained for independent and m dependent input data

some heuristic methods for solving p median problems with a coverage constraint abstract the aim of this paper is to solve p median problems with an additional coverage constraint these problems arise in location applications when the trade off between distance and coverage is being calculated three kinds of heuristic algorithms are developed first local search procedures are designed both for constructing and improving feasible solutions second a multistart grasp heuristic is developed based on the previous local search methods third by employing lagrangean relaxation methods a very efficient lagrangean heuristic algorithm is designed which extends the well known algorithm of handler and zang for constrained shortest path problems to constrained p median problems finally a comparison of the computational efficiency of the developed methods is made between a variety of problems of different sizes

an algorithm for set covering problem in this paper we present an algorithm for the set covering problem that combines problem reduction tests with dual ascent subgradient optimisation and linear programming computational results are presented for problems involving up to 400 rows and 4000 columns

optimal dual frames for erasures for any given frame for the purpose of encoding in a finite dimensional hilbert space we investigate its dual frames that are optimal for erasures for the purpose of decoding we show that in general the canonical dual is not necessarily optimal moreover optimal dual frames are not necessarily unique we present some sufficient conditions under which the canonical dual is the unique optimal dual frame for the erasure problem as an application we get that the canonical dual is the only optimal dual when either the frame is induced by a group representation or the frame is uniform tight

the optimal diversity management problem in some industries a certain part can be needed in a very large number of different configurations this is the case e g for the electrical wirings in european car factories a given configuration can be replaced by a more complete therefore more expensive one the diversity management problem consists of choosing an optimal set of some given number k of configurations that will be produced any nonproduced configuration being replaced by the cheapest produced one that is compatible with it we model the problem as an integer linear program our aim is to solve those problems to optimality the large scale instances we are interested in lead to difficult lp relaxations which seem to be intractable by the best direct methods currently available most of this paper deals with the use of lagrangean relaxation to reduce the size of the problem in order to be able subsequently to solve it to optimality via classical integer optimization

frames of uniform subframe bounds with applications to erasures abstract we introduce a class of frames called usb frames frames of uniform subframe bounds which mean that any subsequence of the frame is a frame for the subspace it spans and the frame bounds depend only on the cardinality of the subsequence we give several necessary and sufficient conditions for a frame to be a usb frame as an application we show that a tight usb frame is optimal for erasures in the sense that the reconstruction error is independent of the position of erasures we give several explicit construction of usb frames