a projection method for l p norm location allocation problems we present a solution method for location allocation problems involving thel p norm where 1 p the method relaxes the 0 1 constraints on the allocations and solves for both the locations and allocations simultaneously necessary and sufficient conditions for local minima of the relaxed problem are stated and used to develop an iterative algorithm this algorithm finds a stationary point on a series of subspaces defined by the current set of activities the descent direction is a projection onto the current subspace of a direction incorporating second order information for the locations and first order information for the allocations under mild conditions the algorithm finds local minima with 0 1 allocations and exhibits quadratic convergence an implementation that exploits the special structure of these problems to dramatically reduce the computational cost of the required numerical linear algebra is described numerical results for thirty six test problems are included

a branch and bound method for the fixed charge transportation problem in this paper we develop a new conditional penalty for the fixed charge transportation problem this penalty is stronger than both the driebeek penalties and the lagrangean penalties of cabot and erenguc computational testing shows that the use of these penalties leads to significant reductions in enumeration and solution times for difficult problems in the size range tested we also study the effect of problem parameters on the difficulty of the problem the ratio of fixed charges to variable costs the shape of the problem arc density in the underlying network and fixed charge arc density are shown to have a significant effect on problem difficulty for problems involving up to 40 origins and 40 destinations

a network penalty method we consider the minimum cost network flow problem and describe how the non linear penalty function methods of conn and bartels can be specialized to a combinatorial algorithm for this problem we report on preliminary computational results which show that this method can require fewer pivots than the simplex method while the amount of work required for each pivot is comparable the algorithm can be proven finite using a modification of cunningham s strongly feasible basis pivoting rule

an efficient newton barrier method for minimizing a sum of euclidean norms a new newton barrier method is proposed for minimizing a sum of euclidean norms msn f x sum i 1 k a i t x b i 2 msn is a nonsmooth problem because f is not differentiable at any point x where any of the norms is zero the method used is based on approximating f with a smooth function which in the limit has the same optimal value as f msn is shown to have a dual problem with properties very similar to duality theory in linear programming this is used in the development of the method and to give a proof of when an optimal solution for the smooth approximation is epsilon optimal measured in the duality gap for the original problem an implementation of the algorithm is described for large sparse problems and numerical results are presented for problems with more than 270 000 nonlinear variables these problems arise from plastic collapse analysis

spatial and behavioral types in the pi calculus we present a framework that combines ideas from spatial logics and behavioral type systems type systems for the pi calculus are proposed where newly declared restricted names are annotated with spatial process properties predicating on those names that are expected to hold in the scope of the declaration types are akin to ccs terms and account for the process abstract behavior and shallow spatial structure type checking relies on spatial model checking but properties are checked against types rather than against processes type soundness theorems ensure that for a certain class of spatial properties well typed programs are also well annotated in the sense that processes in the scope of any restriction do satisfy the corresponding annotation at run time the considered class of properties is rather general differently from previous proposals it includes both safety and liveness ones and is not limited to invariants we also elaborate a distinction between locally and globally checkable properties

the hirsch conjecture for dual transportation polyhedra an algorithm is given that joins any pair of extreme points of a dual transportation polyhedron by a path of at most m 1 n 1 extreme edges

an optimization algorithm for the vehicle routing problem with time windows based on lagrangian relaxation our paper presents a new optimization method for the vehicle routing problem with time windows vrptw the vrptw is a generalization of the vehicle routing problem where the service of a customer must start within a given time interval a so called time window our method is based on a lagrangian relaxation of the constraint set requiring that each customer must be serviced the master problem consists of finding the optimal lagrangian multipliers and the subproblem is a shortest path problem with time windows and capacity constraints the optimal multipliers are found using a method exploiting the benefits of subgradient methods as well as a bundle method the method has been implemented and tested on a series of well known benchmark problems of size up to 100 customers our algorithm turns out to be very competitive compared to algorithms considered in the literature and we have succeeded in solving several previously unsolved problems

a simplex algorithm for piecewise linear programming i derivation and proof the simplex method for linear programming can be extended to permit the minimization of any convex separable piecewise linear objective subject to linear constraints this three part paper develops and analyzes a general computationally practical simplex algorithm for piecewiselinear programming

branch and price column generation for solving huge integer programs we discuss formulations of integer programs with a huge number of variables and their solution by column generation methods i e implicit pricing of nonbasic variables to generate new columns or to prove lp optimality at a node of the branch and bound tree we present classes of models for which this approach decomposes the problem provides tighter lp relaxations and eliminates symmetry we then discuss computational issues and implementation of column generation branch and bound algorithms including special branching rules and efficient ways to solve the lp relaxation we also discuss the relationship with lagrangian duality

a projected newton method for l p norm location problems this paper is concerned with the numerical solution of continuous minisum multifacility location problems involving thel p norm where 1 p x this class of problems is potentially difficult to solve because the objective function is not everywhere diflerentiable after developing conditions that characterize the minimum of the problems under consideration a second order algorithm is presented this algorithm is based on the solution of a finite sequence of linearly constrained subproblems descent directions for these subproblems are obtained by projecting the newton direction onto the corresponding constraint manifold univariate minimization is achieved via a specialized linesearch which recognizes the possibility of first derivative discontinuity and second derivative unboundedness at points along the search direction the algorithm motivated by earlier works of calamai and conn and related to methods recently described by overton and dax is shown to possess both global and quadratic convergence properties degeneracy can complicate the numerical solution of the subproblems this degeneracy is identified and a method for handling it is outlined an implementation of the algorithm that exploits the intrinsic structure of the location problem formulation is then described along with a discussion of numerical results

a feasible descent cone method for linearly constrained minimization problems abstract an improvement over an earlier feasible directions minimization algorithm is presented in a certain sense the new feasible descent cone algorithm is shown to be a generalization of rosen s gradient projection method the algorithm is evaluated for linear programming test problems and promising results are obtained for random problems and problems involving weight minimization of plane trusses

multisets and structural congruence of the pi calculus with replication in the calculus with replication two processes are multiset congruent if they have the same semantics in the multiset transition system m it is proved that extended structural congruence is the same as multiset congruence and that it is decidable

combined lp and quasi newton methods for minimax optimization we present an algorithm for minimax optimization that combines lp methods and quasi newton methods the quasi newton algorithm is used only if an irregular solution is detected in which case second order derivative information is needed in order to obtain a fast final rate of convergence we prove that the algorithm can converge only to a stationary point and that normally the final rate of convergence will be either quadratic or superlinear the performance is illustrated through some numerical examples

the worst additive noise under a covariance constraint the maximum entropy noise under a lag p autocorrelation constraint is known by burg s theorem to be the pth order gauss markov process satisfying these constraints the question is what is the worst additive noise for a communication channel given these constraints is it the maximum entropy noise the problem becomes one of extremizing the mutual information over all noise processes with covariances satisfying the correlation constraints r sub 0 r sub p for high signal powers the worst additive noise is gauss markov of order p as expected but for low powers the worst additive noise is gaussian with a covariance matrix in a convex set which depends on the signal power

the non regular ceo problem we consider the ceo problem for non regular source distributions such as uniform or truncated gaussian a group of agents observe independently corrupted versions of data and transmit coded versions over rate limited links to a ceo the ceo then estimates the underlying data based on the received coded observations agents are not allowed to convene before transmitting their observations this formulation is motivated by the practical problem of a firm s ceo estimating non regular beliefs about a sequence of events before acting on them agents observations are modeled as jointly distributed with the underlying data through a given conditional probability density function we study the asymptotic behavior of the minimum achievable mean squared error distortion at the ceo in the limit when the number of agents l and the sum rate r tend to infinity we establish a 1 r 2 convergence of the distortion an intermediate regime of performance between the exponential behavior in discrete ceo problems berger zhang and viswanathan 1996 and the 1 r behavior in gaussian ceo problems viswanathan and berger 1997 achievability is proved by a layered architecture with scalar quantization distributed entropy coding and midrange estimation the converse is proved using the bayesian chazan zakai ziv bound

a new optimization algorithm for the vehicle routing problem with time windows the vehicle routing problem with time windows vrptw is a generalization of the vehicle routing problem where the service of a customer can begin within the time window defined by the earliest and the latest times when the customer will permit the start of service in this paper we present the development of a new optimization algorithm for its solution the lp relaxation of the set partitioning formulation of the vrptw is solved by column generation feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming the lp solution obtained generally provides an excellent lower bound that is used in a branch and bound algorithm to solve the integer set partitioning formulation our results indicate that this algorithm proved to be successful on a variety of practical sized benchmark vrptw test problems the algorithm was capable of optimally solving 100 customer problems this problem size is six times larger than any reported to date by other published research

the rate distortion region for multiple descriptions without excess rate during recent years there has been strong interest in a certain source coding problem which some authors call the problem of multiple descriptions old and new wringing techniques enable us to establish a single letter characterization of the rate distortion region in the case of no excess rate for the joint description

rate region of the quadratic gaussian two encoder source coding problem we determine the rate region of the quadratic gaussian two encoder source coding problem this rate region is achieved by a simple architecture that separates the analog and digital aspects of the compression furthermore this architecture requires higher rates to send a gaussian source than it does to send any other source with the same covariance our techniques can also be used to determine the sum rate of some generalizations of this classical problem our approach involves coupling the problem to a quadratic gaussian ldquoceo problem rdquo

a structure exploiting algorithm for nonlinear minimax problems in this paper some basic concepts are generalised which characterise the best linear chebyshev approximation in one variable to general nonlinear minimax problems a new method for solving a nonlinear minimax problem is presented which exploits the structure and characterisation of the solution whenever possible the algorithm is globally convergent with a superlinear convergence rate numerical results indicate the efficacy of the new method

an outer approximate subdifferential method for piecewise affine optimization piecewise affine functions arise from lagrangian duals of integer programming problems and optimizing them provides good bounds for use in a branch and bound method methods such as the subgradient method and bundle methods assume only one subgradient is available at each point but in many situations there is more information available we present a new method for optimizing such functions which is related to steepest descent but uses an outer approximation to the subdifferential to avoid some of the numerical problems with the steepest descent approach we provide convergence results for a class of outer approximations and then develop a practical algorithm using such an approximation for the compact dual to the linear programming relaxation of the uncapacitated facility location problem we make a numerical comparison of our outer approximation method with the projection method of conn and cornuejols and the bundle method of schramm and zowe

global convergence of rosen s gradient projection method the convergence of rosen s gradient method is a long standing problem in nonlinear programming recently progress has been made by several researchers in this paper we completely resolve the problem

some facets of the simple plant location polytope we relate the simple plant location problem to the vertex packing problem and derive several classes of facets of their associated integer polytopes

a new method for optimal truss topology design truss topology optimization formulated in terms of displacements and bar volumes results in a large nonconvex optimization problem for the case of maximization of stiffness for a prescribed volume this paper presents a new equivalent an unconstrained and convex minimization problem in displacements only where the function to be minimized is the sum of terms each of which is the maximum of two convex quadratic functions existence of solutions is proved as is the convergence of a nonsmooth steepest descent type algorithm for solving the topology optimization problem the algorithm is computationally attractive and has been tested on a large number of examples some of which are presented

on the exact solution of large scale simple plant location problems abstract the simple plant location problem deals with the selection of facility sites from a set of possible locations with the intention of serving a given set of customers from the chosen locations the objective is to minimize the sum of the fixed charges for establishing the facilities and the transportation costs corresponding to the supply of the demands we show how to modify a primal dual version of erlenkotter s exact algorithm to get an improved procedure computational experience with large scale problems indicates that compared with erlenkotter s code an implementation of the modified algorithm is faster by more than one order of magnitude for real life problems with 1500 potential facility sites the increase of computational speed may even exceed the factor of 100

a simplex algorithm for piecewise linear programming 11 finiteness feasibility and degeneracy the simplex method for linear programming can be extended to permit the minimization of any convex separable piecewise linear objective subject to linear constraints part i of this paper has developed a general and direct simplex algorithm for piecewise linear programming under convenient assumptions that guarantee a finite number of basic solutions existence of basic feasible solutions and nondegeneracy of all such solutions part ii now shows how these assumptions can be weakened so that they pose no obstacle to effective use of the piecewise linear simplex algorithm the theory of piecewise linear programming is thereby extended and numerous features of linear programming are generalized or are seen in a new light an analysis of the algorithm s computational requirements and a survey of applications will be presented in part iii

a convergence theorem of rosen s gradient projection method since rosen s gradient projection method was published in 1960 a rigorous convergence proof of his method has remained an open question a convergence theorem is given in this paper

a version of the bundle idea for minimizing a nonsmooth function conceptual idea convergence analysis numerical results during recent years various proposals for the minimization of a nonsmooth functional have been made amongst these the bundle concept turned out to be an especially fruitful idea based on this concept a number of authors have developed codes that can successfully deal with nonsmooth problems the aim of the paper is to show that by adding some features of the trust region philosophy to the bundle concept the end result is a distinguished member of the bundle family with a more stable behaviour than some other bundle versions the reliability and efficiency of this code is demonstrated on the standard academic test examples and on some real life problems

an efficient primal dual interior point method for minimizing a sum of euclidean norms the problem of minimizing a sum of euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature this nonsmooth optimization problem arises in many different kinds of modern scientific applications we derive a primal dual interior point algorithm for the problem by applying newton s method directly to a system of nonlinear equations characterizing primal and dual feasibility and a perturbed complementarity condition the main work at each step consists of solving a system of linear equations the schur complement equations this schur complement matrix is not symmetric unlike in linear programming we incorporate a mehrotra type predictor corrector scheme and present some experimental results comparing several variations of the algorithm including as one option explicit symmetrization of the schur complement with a skew corrector term we also present results obtained from a code implemented to solve large sparse problems using a symmetrized schur complement this has been applied to problems arising in plastic collapse analysis with hundreds of thousands of variables and millions of nonzeros in the constraint matrix the algorithm typically finds accurate solutions in less than 50 iterations and determines physically meaningful solutions previously unobtainable

automatic decrease of the penalty parameter in exact penalty function methods this paper presents an analysis of the involvement of the penalty parameter in exact penalty function methods that yields modifications to the standard outer loop which decreases the penalty parameter typically dividing it by a constant the procedure presented is based on the simple idea of making explicit the dependence of the penalty function upon the penalty parameter and is illustrated on a linear programming problem with the l1 exact penalty function and an active set approach the procedure decreases the penalty parameter when needed to the maximal value allowing the inner minimization algorithm to leave the current iterate it moreover avoids unnecessary calculations in the iteration following the step in which the penalty parameter is decreased we report on preliminary computational results which show that this method can require fewer iterations than the standard way to update the penalty parameter this approach permits a better understanding of the performance of exact penalty methods

a globally and superlinearly convergent algorithm for convex quadratic programs with simple bbounds a globally and superlinearly convergent algorithm for solving convex quadratic programs with simple bounds is presented the algorithm is developed using a new formulation of the problem the minimization of an unconstrained piecewise quadratic function that has the same optimality conditions as the original problem the major work at each iteration is the cholesky factorization of a positive definite matrix with the size and structure of the hessian of the quadratic hence the algorithm is suitable for solving large sparse problems and for implementation on parallel computers the numerical results indicate that the new approach has promise

structural inclusion in the pi calculus with replication three notions of structural inclusion between process terms of the calculus are considered and proven to be decidable and to have axiomatizations that are sound and complete in the multiset semantics m of the calculus all three are strong simulation relations

a simplex algorithm for piecewise linear programming iii computational analysis and application the first two parts of this paper have developed a simplex algorithm for minimizing convex separable piecewise linear functions subject to linear constraints this concluding part argues that a direct piecewiselinear simplex implementation has inherent advantages over an indirect approach that relies on transformation to a linear program the advantages are shown to be implicit in relationships between the linear and piecewise linear algorithms and to be independent of many details of implementation two sets of computational results serve to illustarate these arguments the piecewise linear simplex algorithm is observed to run 2 6 times faster than a comparable linear algorithm not including any additional expense that might be incurred in setting up the equivalent linear program further support for the practical value of a good piecewise linear programming algorithm is provided by a survey of many varied applications

vector gaussian multiple description with two levels of receivers the problem of l multiple descriptions of a stationary and ergodic gaussian source with two levels of receivers is investigated each of the first level receivers receive an arbitrary subset k of the l descriptions k l the second level receiver receives all l descriptions all the receivers both at the first level and the second level reconstruct the source using the subset of descriptions they receive the corresponding reconstructions are subject to quadratic distortion constraints our main result is the derivation of an outer bound on the sum rate of the descriptions so that the distortion constraints are met we show that an analog digital separation architecture involving joint gaussian vector quantizers and a binning scheme meets this outer bound with equality for several scenarios these scenarios include the case when the distortion constraints are symmetric and the case for general distortion constraints with k 2 and l 3

discontinuous optimization by smoothing we present a simple tool for solving many discontinuous optimization problems the basic idea is to express discontinuities by means of a step function and then to approximate the step function by a smooth one this way a smooth once or twice continuously differentiable approximate problem is obtained this problem can be solved by any gradient technique the approximations introduced contain a single parameter which controls their accuracy so that the original problem is replaced only in some neighborhoods of the points of discontinuity some convergence properties are established and numerical experiments with some test problems are reported

achievable rates for multiple descriptions consider a sequence of independent identically distributed i i d random variables x l x 2 cdots x n and a distortion measure d x i x i on the estimates x i of x i two descriptions i x in 1 2 cdots 2 nr 1 and j x in 1 2 cdots 2 nr 2 are given of the sequence x x 1 x 2 cdots x n from these two descriptions three estimates i x x2 j x and hat x o i x j x are formed with resulting expected distortions e frac 1 n sum n k 1 d x k hat x mk d m m 0 1 2 we find that the distortion constraints d 0 d 1 d 2 are achievable if there exists a probability mass distribution p x p hat x 1 hat x 2 hat x 0 x with ed x hat x m leq d m such that r 1 i x hat x 1 r 2 i x hat x 2 where i cdot denotes shannon mutual information these rates are shown to be optimal for deterministic distortion measures

lattices for distributed source coding jointly gaussian sources and reconstruction of a linear function consider a pair of correlated gaussian sources x 1 x 2 two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder the decoder is interested in reconstructing a linear combination of x 1 and x 2 to within a mean square distortion of d we obtain an inner bound to the optimal rate distortion region for this problem a portion of this inner bound is achieved by a scheme that reconstructs the linear function directly rather than reconstructing the individual components x 1 and x 2 first this results in a better rate region for certain parameter values our coding scheme relies on lattice coding techniques in contrast to more prevalent random coding arguments used to demonstrate achievable rate regions in information theory we then consider the case of linear reconstruction of k sources and provide an inner bound to the optimal rate distortion region some parts of the inner bound are achieved using the following coding structure lattice vector quantization followed by ldquocorrelatedrdquo lattice structured binning

piecewise linear multicriteria programs the continuous case and its discontinuous generalization in this paper we study piecewise linear multicriteria programs that is multicriteria programs with either a continuous or discontinuous piecewise linear objective function and a polyhedron set constraint we obtain an algebraic representation of a semi closed polyhedron and apply it to show that the image of a semi closed polyhedron under a continuous linear function is always one semi closed polyhedron we establish that the weak pareto solution point set of a piecewise linear multicriteria program is the union of finitely many semi closed polyhedra we propose an algorithm for finding the pareto point set of a continuous piecewise linear bi criteria program and generalize it to the discontinuous case we apply our algorithm to solve the discontinuous bi criteria portfolio selection problem with an l risk measure and transaction costs and show that this algorithm can be improved by using an ideal point strategy

on the solution of highly degenerate linear programs the solution of scheduling problems often gives rise to highly degenerate linear programmes which cause significant computational difficulties for the revised simplex method wolfe s highly effective ad hoc method for overcoming the cycling or stalling problems associated with degeneracy is described here it is given a geometric interpretation in terms of finding a direction of recession for a reduced problem which is fundamental to a full understanding of the procedure an example of an aircrew scheduling problem is used to illustrate the effectiveness of the method

a hybrid multistart heuristic for the uncapacitated facility location problem we present a multistart heuristic for the uncapacitated facility location problem based on a very successful method we originally developed for the p median problem we show extensive empirical evidence to the effectiveness of our algorithm in practice for most benchmarks instances in the literature we obtain solutions that are either optimal or a fraction of a percentage point away from it even for pathological instances created with the sole purpose of being hard to tackle our algorithm can get very close to optimality if given enough time it consistently outperforms other heuristics in the literature

primal methods are better than dual methods for solving overdetermined linear systems in the l sense it is generally believed that methods based upon solving the dual of the linear programming formulation of the linear l infty problem are superior to methods based upon the primal formulation a primal approach is presented along with evidence that for random problems primal methods are to be preferred it is then shown that the method generally considered to be the best algorithm for discrete linear approximation in the l infty norm actually owes much of its efficiency to effective choice of a starting point this phenomenon is explained with the aid of results from classical minimax theory which are then used to determine a suitable initial point for a primal method with this enhancement it would appear that the primal approach is also preferable for problems arising from function approximations

a trust region algorithm for nonsmooth optimization a trust region algorithm is proposed for minimizing the nonsmooth composite functionf x h f x wheref is smooth andh is convex the algorithm employs a smoothing function which is closely related to fletcher s exact differentiable penalty functions global and local convergence results are given considering convergence to a strongly unique minimizer and to a minimizer satisfying second order sufficiency conditions

exact penalty functions in constrained optimization in this paper formal definitions of exactness for penalty functions are introduced and sufficient conditions for a penalty function to be exact according to these definitions are stated thus providing a unified framework for the study of both nondifferentiable and continuously differentiable penalty functions in this framework the best known classes of exact penalty functions are analyzed and new results are established concerning the correspondence between the solutions of the constrained problem and the unconstrained minimizers of the penalty functions

sum rate of the vacationing ceo problem the vacationing chief executive officer ceo problem combines the salient features of the so called ceo problem and the multiple description md problem in this setting noisy versions of a source are observed by two encoders as in the ceo problem in addition we require that each encoder generate mds of the source as in the md problem the vacationing ceo problem arises in asynchronous multicast networks and solving it is an essential step in developing a general theory for multiencoder and multidecoder lossy compression in this paper an achievable sum rate and two sum rate lower bounds are presented for the quadratic gaussian vacationing ceo problem these bounds exactly determine the optimal sum rate over a wide range of parameters

a globally and quadratically convergent affine scaling method for linear e 1 problems recently various interior point algorithms related to the karmarkar algorithm have been developed for linear programming in this paper we first show how this interior point philosophy can be adapted to the linear l1 problem in which there are no feasibility constraints to yield a globally and linearly convergent algorithm we then show that the linear algorithm can be modified to provide aglobally and ultimatelyquadratically convergent algorithm this modified algorithm appears to be significantly more efficient in practise than a more straightforward interior point approach via a linear programming formulation we present numerical results to support this claim

the rate distortion function for the quadratic gaussian ceo problem a new multiterminal source coding problem called the ceo problem was presented and investigated by berger zhang and viswanathan recently viswanathan and berger have investigated an extension of the ceo problem to gaussian sources and call it the quadratic gaussian ceo problem they considered this problem from a statistical viewpoint deriving some interesting results in this paper we consider the quadratic gaussian ceo problem from a standpoint of multiterminal rate distortion theory we regard the ceo problem as a certain multiterminal remote source coding problem with infinitely many separate encoders whose observations are conditionally independent if the remote source is given this viewpoint leads us to a complete solution to the problem we determine the tradeoff between the total amount of rate and squared distortion deriving an explicit formula of the rate distortion function the derived function has the form of a sum of two nonnegative functions one is a classical rate distortion function for single gaussian source and the other is a new rate distortion function which dominates the performance of the system for a relatively small distortion it follows immediately from our result that the conjecture of viswanathan and berger on the asymptotic behavior of minimum squared distortion for large rates is true

a new approach for crew pairing problems by column generation with an application to air transportation we propose a new approach to crew pairing problems arising in the context of airline companies the problem is first formulated as a large scale set covering problem with many colums each column representing a valid crew pairing we then suggest a solution procedure for the continuous relaxation of this large scale problem based on generalized linear programming in which the column generation subproblem is shown to be equivalent to a shortest path problem in an associated graph computational results obtained on a series of real problems involving up to 329 flight segments are reported confirming both computational efficiency and practical applicability of the new approach indeed not only were the resulting solutions observed to be integral for most test problems but average savings of about 4 to 5 over the best available hand built solutions were shown to be obtained

distribution systems design with role dependent objectives in this paper we introduce flexible models for capacitated discrete location problems we describe three different points of view of a location problem in a logistics system different mathematical programming formulations are presented illustrated by examples and compared using a battery of test problems extensive computational tests are done showing the potentials and limits of this kind of resolution approach

vector gaussian multiple description with individual and central receivers t multiple descriptions of a vector gaussian source for individual and central receivers are investigated the sum rate of the descriptions with covariance distortion measure constraints in a positive semidefinite ordering is exactly characterized for two descriptions the entire rate region is characterized the key component of the solution is a novel information theoretic inequality that is used to lower bound the achievable multiple description rates jointly gaussian descriptions are optimal in achieving the limiting rates we also show the robustness of this description scheme the distortions achieved are no larger when used to describe any non gaussian source with the same covariance matrix

local properties of algorithms for minimizing nonsmooth composite functions this paper considers local convergence and rate of convergence results for algorithms for minimizing the composite functionf x f x h c x wheref andc are smooth buth c may be nonsmooth local convergence at a second order rate is established for the generalized gauss newton method whenh is convex and globally lipschitz and the minimizer is strongly unique local convergence at a second order rate is established for a generalized newton method when the minimizer satisfies nondegeneracy strict complementarity and second order sufficiency conditions assuming the minimizer satisfies these conditions necessary and sufficient conditions for a superlinear rate of convergence for curvature approximating methods are established necessary and sufficient conditions for a two step superlinear rate of convergence are also established when only reduced curvature information is available all these local convergence and rate of convergence results are directly applicable to nonlinearing programming problems

linear programming the simplex algorithm and simple polytopes in the first part of the paper we survey some far reaching applications of the basic facts of linear programming to the combinatorial theory of simple polytopes in the second part we discuss some recent developments concerning the simplex algorithm we describe subexponential randomized pivot rules and upper bounds on the diameter of graphs of polytopes 1997 the mathematical programming society inc published by elsevier science b v

nonlinear programming via an exact penalty function global analysis in this paper we motivate and describe an algorithm to solve the nonlinear programming problem the method is based on an exact penalty function and possesses both global and superlinear convergence properties we establish the global qualities here the superlinear nature is proven in 7 the numerical implementation techniques are briefly discussed and preliminary numerical results are given

probabilistic analysis of a relaxation for the k median problem this paper provides a probabilistic analysis of the so called strong linear programming relaxation of the k median problem when the number of points say n goes to infinity the analysis is performed under four classical models in location theory the euclidean network tree and uniform cost models for example we show that for the euclidean model and k k o n log n the value of the relaxation is almost surely within 0 3 percent of the optimum k median value for the uniform cost model and the same conditions on k we show that the value of the relaxation is almost surely 50 percent of the optimum k median value we also show that under various assumptions branch and bound algorithms that use the strong linear programming relaxation as a bound must almost surely expand a nonpolynomial number of nodes to solve the k median problem to optimality finally we report extensive computational experiments as predicted by the probabilistic analysis the relaxation was not as tight for the problem

a dynamic subgradient based branch and bound procedure for set covering we discuss a branch and bound algorithm for set covering whose centerpiece is a new integrated upper bounding lower bounding procedure called dynamic subgradient optimization dynsgrad this new procedure applied to a lagrangean dual at every node of the search tree combines the standard subgradient method with primal and dual heuristics that interact to change the lagrange multipliers and tighten the upper and lower bounds fix variables and periodically restate the lagrangean itself extensive computational testing is reported as a stand alone heuristic dynsgrad performs significantly better than other procedures in terms of the quality of solutions obtainable with a certain computational effort when incorporated into a branch and bound algorithm dynsgrad considerably advances the state of the art in solving set covering problems

on the uncapacitated plant location problem ii facets and lifting theorems several lifting procedures for facets of the uncapacitated plant location problem are discussed also necessary and sufficient conditions for nontrivial facets with 0 1 integer coefficients are derived in addition all of the facets for the case of three or more plants and three destinations are identified

a conjugate rosen s gradient projection method with global line search for piecewise linear concave optimization abstract the kelley cutting plane method is one of the methods commonly used to optimize the dual function in the lagrangian relaxation scheme usually the kelley cutting plane method uses the simplex method as the optimization engine it is well known that the simplex method leaves the current vertex follows an ascending edge and stops at the nearest vertex what would happen if one would continue the line search up to the best point instead as a possible answer we propose the face simplex method which freely explores the polyhedral surface by following the rosen s gradient projection combined with a global line search on the whole surface furthermore to avoid the zig zagging of the gradient projection we propose a conjugate gradient version of the face simplex method for our preliminary numerical tests we have implemented this method in matlab this implementation clearly outperforms basic matlab implementations of the simplex method in the case of state of the art simplex implementations in c or similar our matlab implementation is only competitive for the case of many cutting planes

the many facets of linear programming we examine the history of linear programming from computational geometric and complexity points of view looking at simplex ellipsoid interior point and other methods

a projection method for the uncapacitated facility location problem several algorithms already exist for solving the uncapacitated facility location problem the most efficient are based upon the solution of the strong linear programming relaxation the dual of this relaxation has a condensed form which consists of minimizing a certain piecewise linear convex function this paper presents a new method for solving the uncapacitated facility location problem based upon the exact solution of the condensed dual via orthogonal projections the amount of work per iteration is of the same order as that of a simplex iteration for a linear program inm variables and constraints wherem is the number of clients for comparison the underlying linear programming dual hasmn m n variables andmn n constraints wheren is the number of potential locations for the facilities the method is flexible as it can handle side constraints in particular when there is a duality gap the linear programming formulation can be strengthened by adding cuts numerical results for some classical test problems are included

a global and quadratically convergent method for linear l problems a new globally and quadratically convergent algorithm is proposed for the linear l infty problem this method works on the piecewise linear l infty problem directly by generating descent directions via a sequence of weighted least squares problems and using a piecewise linear line search to ensure a decrease in the l infty function at every step it is proven that ultimately full newton like steps are taken where the newton step is based on the complementary slackness condition holding at the solution numerical results suggest a very promising method the number of iterations required to achieve high accuracy is relatively insensitive to problem size

nonlinear programming via an exact penalty function asymptotic analysis in this paper we consider the final stage of a global method to solve the nonlinear programming problem we prove 2 step superlinear convergence in the process of analyzing this asymptotic behavior we compare our method theoretically to the popular successive quadratic programming approach

the plant location problem with demand dependent setup costs and centralized allocation suppose that customers are situated at the nodes of a transportation network and a service company plans to locate a number of facilities that will serve the customers the objective is to minimize the sum of the total setup cost and the total transportation cost the setup cost of a facility is demand dependent that is it depends on the number of customers that are served by the facility centralized allocation of customers to facilities is assumed that is the service company makes a decision about allocation of customers to facilities in the case of a general network the model can be formulated as a mixed integer programming problem for the case of a tree network we develop a polynomial time dynamic programming algorithm

erasure multiple descriptions a binary erasure version of channel multiple descriptions md with symmetric descriptions i e the rates of the descriptions are equal and the distortion constraint depends only on the number of messages received is considered no excess rate for every out of descriptions i e any messages have sum rate where is shannon s rate distortion function for erasure distortion and is the distortion constraint to be met is investigated the goal is to characterize the achievable distortions reconstruction fidelity is measured using two criteria a worst case criterion which computes distortion by maximizing the per letter distortion over all source sequences and an average case criterion which computes distortion by averaging the per letter distortion over all source sequences achievability schemes are presented based on systematic maximum distance separable codes for worst case distortion and random binning for average case distortion and optimality results are proved for the corresponding distortion regions the erasure md setup is then used to propose a layered coding framework for multiple descriptions which is then applied to vector gaussian md and shown to be optimal for symmetric scalar gaussian md with two levels of receivers and no excess rate at the central receiver

discontinuous piecewise linear optimization a theoretical framework and a practical algorithm are presented to solve discontinuous piecewise linear optimization problems dealing with functions for which theridges are known a penalty approach allows one to consider such problems subject to a wide range of constraints involving piecewise linear functions although the theory is expounded in detail in the special case of discontinuous piecewiselinear functions it is straightforwardly extendable using standard nonlinear programming techniques tononlinear discontinuous piecewise differentiable functions the descent algorithm which is elaborated uses active set and projected gradient approaches it is a generalization of the ideas used by conn to deal with nonsmoothness in thel1 exact penalty function and it is based on the notion ofdecomposition of a function into a smooth and a nonsmooth part the constrained case is reduced to the unconstrained minimization of a piecewise linear l1 exact penalty function we also discuss how the algorithm is modified when it encounters degenerate points preliminary numerical results are presented the algorithm is applied to discontinuous optimization problems from models in industrial engineering 1998 the mathematical programming society inc published by elsevier science b v

rate region of gaussian multiple description coding with individual and central distortion constraints the rate region of gaussian multiple description coding with individual and central distortion constraints is completely characterized specifically a lower bound and an upper bound are derived for each supporting hyperplane of the rate region where the lower bound is associated with a max min game while the upper bound is associated with a min max game furthermore it is shown that these two bounds coincide due to the existence of a saddle point