relaxation methods for monotropic programs we propose a dual descent method for the problem of minimizing a convex possibly nondifferentiable separable cost subject to linear constraints the method has properties reminiscent of the gauss seidel method in numerical analysis and uses the e complementary slackness mechanism introduced in bertsekas hosein and tseng 1987 to ensure finite convergence to near optimality as special cases we obtain the methods in bertsekas hosein and tseng 1987 for network flow programs and the methods in tseng and bertsekas 1987 for linear programs

minimizers of convex functionals arising in random surfaces we investigate c1 regularity of minimizers to f u dx in two dimensions for certain classes of non smooth convex functionals f in particular our results apply to the surface tensions that appear in recent works on random surfaces and random tilings of kenyon okounkov and others

numerical approximation of electromagnetic signals arising in the evaluation of geological formations the integration of complicated oscillatory functions arises in computational electromagnetics when evaluating signals produced by the propagation of electromagnetic radiation through the anisotropic layers of a geological formation the computation of exact integrals involves the evaluation of sommerfeld integrals the matrix pencil method is used for the numerical approximation of such signals numerical results show accuracy and robustness of the method for the approximation of these signals and efficiency in their numerical integration sampling frequency is discussed and numerical efficiency is improved by down sampling

the weighted averages algorithm revisited the classic weighted averages wa algorithm for the evaluation of sommerfeld like integrals is reviewed and reappraised as a result a new version of the wa algorithm called generalized wa is introduced the new version can be considered as a generalization of the well established holder and cesaro means used to sum divergent series generalized wa exhibits a more compact formulation devoid of iterative and recursive steps and a wider range of applications it is more robust as it provides a unique formulation valid for monotonic and oscillating functions the implementation of the new version is easier and more economical in terms of basic operations preliminary numerical examples show that generalized wa also outperforms in terms of accuracy the classic wa algorithm which is currently recognized as the most competitive algorithm to evaluate sommerfeld integral tails

the distance function from the boundary of a domain with corners abstract we study the regularity of the distance function to the boundary of a domain in r 2 with respect to some asymmetric norms we allow the boundary of the domain to have corners we obtain an explicit formula for the second derivative of these distance functions furthermore we study a generalized notion of the ridge of a domain which is the set of singularities of a distance function to the boundary of the domain we completely characterize the ridge by using a generalized notion of curvature

simultaneous lotsizing and scheduling by combining local search with dual reoptimization abstract the contribution of this paper is twofold on the one hand the particular problem of integrating lotsizing and scheduling of several products on a single capacitated production line is modelled and solved taking into account sequence dependent setup times thereby continuous lotsizes meeting deterministic dynamic demands are to be determined and scheduled with the objective of minimizing inventory holding costs and sequence dependent setup costs on the other hand a new general algorithmic approach is presented a dual reoptimization algorithm is combined with a local search heuristic for solving a mixed integer programming problem this idea is applied to the above lotsizing and scheduling problem by embedding a dual network flow algorithm into threshold accepting and simulated annealing respectively computational tests show the effectiveness of the new solution method

the free boundary of variational inequalities with gradient constraints abstract in this paper we prove that the free boundary of the minimizer of i v u 1 2 d v 2 v d x subject to the pointwise gradient constraint d v p 1 is as regular as the tangent bundle of the boundary of the domain to this end we study a generalized notion of ridge of a domain in the plane which is the set of singularity of the distance function in the p norm to the boundary of the domain

polynomial methods for separable convex optimization in unimodular linear spaces with applications we consider the problem of minimizing a separable convex objective function over the linear space given by a system mx 0 with m a totally unimodular matrix in particular this generalizes the usual minimum linear cost circulation and cocirculation problems in a network and the problems of determining the euclidean distance from a point to the perfect bipartite matching polytope and the feasible flows polyhedron we first show that the idea of minimum mean cycle canceling originally worked out for linear cost circulations by goldberg and tarjan j assoc comput mach 36 1989 pp 873 886 and extended to some other problems t r ervolina and s t mccormick discrete appl math 46 1993 pp 133 165 a frank and a v karzanov technical report rr 895 m laboratoire artemis imag universite joseph fourier grenoble france 1992 t ibaraki a v karzanov and h nagamochi private communication 1993 m hadjiat technical report groupe intelligence artificielle faculte des sciences de luminy marseille france 1994 can be generalized to give a combinatorial method with geometric convergence for our problem we also generalize the computationally more efficient cancel and tighten method we then consider objective functions that are piecewise linear pure and piecewise quadratic or piecewise mixed linear and quadratic and we show how both methods can be implemented to find exact solutions in polynomial time strongly polynomial in the piecewise linear case these implementations are then further specialized for finding circulations and cocirculations in a network we finish by showing how to extend our methods to find optimal integer solutions to linear spaces of larger fractionality and to the case when the objective functions are given by approximate oracles

the discrete lot sizing and scheduling problem abstract the discrete lot sizing and scheduling problem consists in scheduling several products on a single machine so as to meet the known dynamic demand and to minimize the sum of inventory and setup cost the planning interval is phased into many short periods e g shifts or days and setups may occur only at the beginning of a period a branch and bound procedure is presented using lagrangean relaxation for determining both lower bounds and feasible solutions the relaxed problems are solved by dynamic programming computational results on a personal computer are reported for various examples from the literature with up to 12 products and 122 periods or 3 products and 250 periods the procedure yields optimal solutions or at least feasible solutions with tight lower bounds in a few minutes the results are compared with those obtained by solving the usual capacitated lot sizing problem

combinatorial algorithms for the generalized circulation problem we consider a generalization of the maximum flow problem in which the amounts of flow entering and leaving an arc are linearly related more precisely if x e units of flow enter an arc e x e e units arrive at the other end for instance nodes of the graph can correspond to different currencies with the multipliers being the exchange rates we require conservation of flow at every node except a given source node the goal is to maximize the amount of flow excess at the source this problem is a special case of linear programming and therefore can be solved in polynomial time in this paper we present the first polynomial time combinatorial algorithms for this problem the algorithms are simple and intuitive

studying the effects of production loss due to setup in dynamic production scheduling abstract we study the effects of production loss during setup in dynamic production scheduling for process industries producing several products on non identical flexible processors the production scheduling problem is formulated as a mixed integer programming model and solved using primal and dual lagrangean based procedures real data from a tile company and randomly generated data were used to test the model our computational results show the solution procedure to be fast robust and stable even for cases with large setup costs and production losses and for cases with demands of up to 52 periods

computation of the sommerfeld integral tails using the matrix pencil method the oscillating infinite domain sommerfeld integrals si are difficult to integrate using a numerical procedure when dealing with structures in a layered media even though several researchers have attempted to do that generally integration along the real axis is used to compute the si however significant computational effort is required to integrate the oscillating and slowly decaying function along the tail extrapolation methods are generally applied to accelerate the rate of convergence of these integrals however there are difficulties with the extrapolation methods such as locations for the breakpoints in this paper we illustrate a simplified approach for accurate and efficient calculation of the integrals dealing with the tails of the si in this paper we fit the tail by a sum of finite usually 10 to 20 complex exponentials using the matrix pencil method mpm the integral of the tail of the si is then simply calculated by summing some complex numbers no numerical integration is needed in this process as the integrals can be done analytically good accuracy is achieved with a small number of evaluations for the integral kernel 60 points for the mpm as compared with hundreds or thousands of functional evaluations using the traditional extrapolation methods along the tails of the si simulation results show that to obtain the similar accuracy in the evaluation of the si the mpm is approximately 10 times faster than the traditional extrapolation methods moreover since the mpm is robust to the effects of noise this method is more stable especially for large values of the horizontal distances the method proposed in this paper is thus a new and better technique to obtain accurate results for the computation of the green s function for a layered media in the spatial domain

lotsizing and scheduling on parallel machines with sequence dependent setup costs industrial lotsizing and scheduling pose very difficult analytical problems we propose an unconventional model that deals with sequence dependent setup costs in a multiple machine environment the sequence splitting model splits an entire schedule into subsequences leading to tractable subproblems an optimization approach based on a column generation branch and bound methodology is developed and heuristically adapted to test problems including five real world problem instances gathered from industry

threshold accepting a general purpose optimization algorithm appearing superior to simulated annealing abstract a new general purpose algorithm for the solution of combinatorial optimization problems is presented the new threshold accepting method is even simpler structured than the wellknown simulated annealing approach the power of the new algorithm is demonstrated by computational results concerning the traveling salesman problem and the problem of the construction of error correcting codes moreover deterministic versions of the new heuristic turn out to perform nearly equally well consuming only a fraction of the computing time of the stochastic versions as an example the deterministic threshold accepting method yields very near to optimum tours for the famous 442 cities traveling salesman problem of grotschel within 1 to 2 s of cpu time

new algorithms for generalized network flows this paper of which a preliminary version appeared in istcs 92 is concerned with generalized network flow problems in a generalized network each edgee u v has a positive flow multiplier a e associated with it the interpretation is that if a flow ofx e enters the edge at nodeu then a flow ofa e x e exits the edge atv the uncapacitated generalized transshipment problem ugt is defined on a generalized network where demands and supplies real numbers are associated with the vertices and costs real numbers are associated with the edges the goal is to find a flow such that the excess or deficit at each vertex equals the desired value of the supply or demand and the sum over the edges of the product of the cost and the flow is minimized adler and cosares operations research 39 1991 955 960 reduced the restricted uncapacitated generalized transshipment problem where only demand nodes are present to a system of linear inequalities with two variables per inequality the algorithms presented by the authors in siam journal on computing to appear result in a faster algorithm for restricted ugt generalized circulation is defined on a generalized network with demands at the nodes and capacity constraints on the edges i e upper bounds on the amount of flow the goal is to find a flow such that the excesses at the nodes are proportional to the demands and maximized we present a new algorithm that solves the capacitated generalized flow problem by iteratively solving instances of ugt the algorithm can be used to find an optimal flow or an approximation thereof when used to find a constant factor approximation the algorithm is not only more efficient than previous algorithms but also strongly polynomial it is believed to be the first strongly polynomial approximation algorithm for generalized circulation the existence of such an approximation algorithm is interesting since it is not known whether the exact problem has a strongly polynomial algorithm

an epsilon relaxation method for separable convex cost network flow problems we propose a new method for the solution of the single commodity separable convex cost network flow problem the method generalizes the epsilon relaxation method developed for linear cost problems and reduces to that method when applied to linear cost problems we show that the method terminates with a near optimal solution and we provide an associated complexity analysis we also present computational results showing that the method is much faster than earlier relaxation methods particularly for ill conditioned problems

rational modeling by pencil of functions method pole zero modeling of signals such as an electromagnetic scatterer response is considered in this paper it is shown by use of the pencil of functions theorem that a the true parameters can be recovered in the ideal case where the signal is the impulse reponse of a rational function h z and b the parameters are optimal in the functional dependence sense when the observed data are corrupted by additive noise or by systematic error although the computations are more involved than in all pole modeling they are considerably less than those required in iterative schemes of pole zero modeling the advantages of the method are demonstrated by a simulation example and through application to the electromagnetic response of a scatterer the paper also includes very recent and promising results on a new approach to noise correction in contradistinction with spectral subtraction techniques where only amplitude information is emphasized and phase is ignored we propose a method that a estimates the noise spectral density for the data frame and then b performs the subtraction of the noise correlation matrix from the gram matrix of the signal

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

a polynomial time descent method for separable convex optimization problems with linear constraints we propose a polynomial algorithm for a separable convex optimization problem with linear constraints we do not make any additional assumptions about the structure of the objective function except for polynomial computability that is the objective function can be non differentiable the running time of our algorithm is polynomial in the size of the input consisting of an instance of the problem and the accuracy with which the problem is to be solved our algorithm uses an oracle for solving auxiliary systems of linear inequalities this oracle can be any polynomial algorithm for linear programming

a decomposition approach for the general lotsizing and scheduling problem for parallel production lines abstract this paper presents a novel solution heuristic to the general lotsizing and scheduling problem for parallel production lines glsppl the glsppl addresses the problem of simultaneously deciding about the sizes and schedules of production lots on parallel heterogeneous production lines with respect to scarce capacity sequence dependent setup times and deterministic dynamic demand of multiple products its objective is to minimize inventory holding sequence dependent setup and production costs the new heuristic iteratively decomposes the multi line problem into a series of single line problems which are easier to solve different approaches for decomposition and for the iteration between a modified multi line master problem and the single line subproblems are proposed they are compared with an existing solution method for the glsppl by means of medium sized and large practical problem instances from different types of industries the new methods prove to be superior with respect to both solution quality and computation time

generalized pencil of function method for extracting poles of an em system from its transient response a generalized pencil of function gpof method is developed for extracting the poles of an electromagnetic system from its transient response the gpof method needs the solution of a generalized eigenvalue problem to find the poles subspace decomposition is also used to optimize the performance of the gpof method the gpof method has advantages over the prony method in both computation and noise sensitivity and approaches the cramer rao bound when the signal to noise ratio snr is above threshold an application of the gpof method to a thin wire target is presented

on svd for estimating generalized eigenvalues of singular matrix pencil in noise several algorithms for estimating generalized eigenvalues ges of singular matrix pencils perturbed by noise are reviewed the singular value decomposition svd is explored as the common structure in the three basic algorithms direct matrix pencil algorithm pro esprit and tls esprit it is shown that several svd based steps inherent in the algorithms are equivalent to the first order approximation in particular the pro esprit and its variant tls pro esprit are shown to be equivalent and the tls esprit and its earlier version ls esprit are shown to be asymptotically equivalent to the first order approximation for the problem of estimating superimposed complex exponential signals the state space algorithm is shown to be also equivalent to the previous matrix pencil algorithms to the first order approximation the second order perturbation and the threshold phenomenon are illustrated by simulation results based on a damped sinusoidal signal an improved state space algorithm is found to be the most robust to noise

the distance function from the boundary in a minkowski space let the space be endowed with a minkowski structure that is is the gauge function of a compact convex set having the origin as an interior point and with boundary of class and let be the asymmetric distance associated to given an open domain of class let be the minkowski distance of a point from the boundary of we prove that a suitable extension of to which plays the role of a signed minkowski distance to is of class in a tubular neighborhood of and that is of class outside the cut locus of that is the closure of the set of points of nondifferentiability of in in addition we prove that the cut locus of has lebesgue measure zero and that can be decomposed up to this set of vanishing measure into geodesics starting from and going into along the normal direction with respect to the minkowski distance we compute explicitly the jacobian determinant of the change of variables that associates to every point outside the cut locus the pair where denotes the unique projection of on and we apply these techniques to the analysis of pdes of monge kantorovich type arising from problems in optimal transportation theory and shape optimization

a strongly polynomial algorithm for a special class of linear programs we extend the list of linear programming problems that are known to be solvable in strongly polynomial time to include a class of lps which contains special cases of the generalized transshipment problem the result is facilitated by exploiting some special properties associated with leontief substitution systems and observing that a feasible solution to the system ax b x 0 in which no variable appears in more than two equations can be found in strongly polynomial time for b belonging to some set

a perturbation property of the tls lp method it is shown that the tls lp total least squares linear prediction method and the svd prony method are equivalent to the first order perturbation approximation in practice it means that the two methods yield the same estimation variances when the signal to noise ratio snr is above a threshold

complex plane generalization of scalar levin transforms a robust rapidly convergent method to compute potentials and fields in multi layered media abstract we propose the complex plane generalization of a powerful algebraic sequence acceleration algorithm the method of weighted averages mwa to guarantee exponential cum algebraic convergence of fourier and fourier hankel f h integral transforms this complex plane mwa effected via a linear path detour in the complex plane results in rapid absolute convergence of field and potential solutions in multi layered environments regardless of the source observer geometry and anisotropy loss of the media present in this work we first introduce a new integration path used to evaluate the field contribution arising from the radiation spectra subsequently we 1 exhibit the foundational relations behind the complex plane extension to a general levin type sequence convergence accelerator 2 specialize this analysis to one member of the levin transform family the mwa 3 address and circumvent restrictions arising for two dimensional integrals associated with wave dynamics problems through minimal complex plane detour restrictions and a novel partition of the integration domain 4 develop and compare two formulations based on standard real axis mwa variants and 5 present validation results and convergence characteristics for one of these two formulations

maximum network flows with concave gains this paper deals with a generalized maximum flow problem with concave gains which is a nonlinear network optimization problem optimality conditions and an algorithm for this problem are presented the optimality conditions are extended from the corresponding results for the linear gain case the algorithm is based on the scaled piecewise linear approximation and on the fat path algorithm described by goldberg plotkin and tardos for linear gain cases the proposed algorithm solves a problem with piecewise linear concave gains faster than the naive solution by adding parallel arcs

meta heuristics for dynamic lot sizing a review and comparison of solution approaches proofs from complexity theory as well as computational experiments indicate that most lot sizing problems are hard to solve because these problems are so difficult various solution techniques have been proposed to solve them in the past decade meta heuristics such as tabu search genetic algorithms and simulated annealing have become popular and efficient tools for solving hard combinatorial optimization problems we review the various meta heuristics that have been specifically developed to solve lot sizing problems discussing their main components such as representation evaluation neighborhood definition and genetic operators further we briefly review other solution approaches such as dynamic programming cutting planes dantzig wolfe decomposition lagrange relaxation and dedicated heuristics this allows us to compare these techniques understanding their respective advantages and disadvantages gives insight into how we can integrate elements from several solution approaches into more powerful hybrid algorithms finally we discuss general guidelines for computational experiments and illustrate these with several examples

an e out of kilter method for monotropic programming the out of kilter method was first proposed by fulkerson 1961 for linear cost network flow and independently by minty 1961 for piecewise linear cost network flow and was then extended by rockafellar 1984 section 11k to piecewise linear cost monotropic programming we propose an extension of this method based on rockafellar s work and on ideas from e relaxation methods for convex cost network flow bertsekas et al 1997a de leone et al 1999 to monotropic programming in general the proposed method is amenable to a complexity analysis and its convergence is based on essentially a monotone decrease in vertical distance to the characteristic curve for each index

surface electric fields and impedance matrix elements of stratified media for the various geometrical configurations of waves in stratified media we consider the important case when both source and field points are located on the same interface separating two different dielectric media we denote this configuration as surface electric field case in this paper the electric fields are calculated numerically without using potentials for the surface electric field case the integrand of the electric field grows with k sub spl rho sup 3 2 for large spl kappa sub spl rho making the sommerfeld integral singular to calculate the surface electric fields in the spatial domain we previously applied a technique of higher order asymptotic extraction in the higher order asymptotic extraction the higher order asymptotic parts were calculated analytically the remainder which has an integrand decays as spl kappa sub spl rho sup 3 2 was calculated numerically along the sommerfeld contour path of integration in this paper we use a different extraction technique the half space extraction after the half space extraction the integrand of the sommerfeld integral of stratified media decays exponentially and the integral is calculated along the sommerfeld integration path the half space extraction part is calculated by numerical integration along the vertical branch cuts the surface electric fields for stratified media using half space extraction and higher order asymptotic extraction are in good agreement to validate the accuracy of the solution we also compute the impedance matrix elements using surface electric fields testing and basis functions all in the spatial domain the results are then compared with the results of the spectral domain method the comparisons of the complex impedance matrix elements are tabulated and show that the difference is less than 2

relaxation methods for network flow problems with convex arc costs we consider the standard single commodity network flow problem with both linear and strictly convex possibly nondifferentiable arc costs for the case where all arc costs are strictly convex we study the convergence of a dual gauss seide type relaxation method that is well suited for parallel computation we then extend this method to the case where some of the arc costs are linear as a special case we recover a relaxation method for the linear minimum cost network flow problem proposed in bertsekas 1 and bertsekas and tseng 2

relaxation methods for minimum cost ordinary and generalized network flow problems we propose a new class of algorithms for linear cost network flow problems with and without gains these algorithms are based on iterative improvement of a dual cost and operate in a manner that is reminiscent of coordinate ascent and gauss seidel relaxation methods we compare our coded implementations of these methods with mature state of the art primal simplex and primal dual codes and find them to be several times faster on standard benchmark problems and faster by an order of magnitude on large randomly generated problems our experiments indicate that the speedup factor increases with problem dimension

faster algorithms for the generalized network flow problem we consider the generalized network flow problem each arc e in the network has a gain factor e if f e units of flow enter arc e then f e e units arrive at the other end of e the objective is to maximize the net flow into one specific node the sink the constraints are the conservation of flow at nodes and the capacities of arcs we present a combinatorial algorithm which solves this problem in o m2 m n log log b log b time where n is the number of nodes m is the number of arcs and b is the largest integer used to represent the gain factors the capacities and the initial supplies at the nodes if m is o n4 3 e and b is not extremely large then our bound is better than the previous best upper bound for this problem we also improve the best known upper bound for the approximate generalized flow problem by showing that a solution whose value is within a factor of 1 from the optimum can be computed in o m m n log log b log 1 time plus o mn2 log b time for preprocessing

extrapolation methods for sommerfeld integral tails a review is presented of the extrapolation methods for accelerating the convergence of sommerfeld type integrals i e semi infinite range integrals with bessel function kernels which arise in problems involving antennas or scatterers embedded in planar multilayered media attention is limited to partition extrapolation procedures in which the sommerfeld integral is evaluated as a sum of a series of partial integrals over finite subintervals and is accelerated by an extrapolation method applied over the real axis tail segment spl alpha spl infin of the integration path where spl alpha 0 is selected to ensure that the integrand is well behaved an analytical form of the asymptotic truncation error or the remainder which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most efficient extrapolation methods is derived several extrapolation algorithms deemed to be the most suitable for the sommerfeld integrals are described and their performance is compared it is demonstrated that the performance of these methods is strongly affected by the horizontal displacement of the source and field points spl rho and by the choice of the subinterval break points furthermore it is found that some well known extrapolation techniques may fail for a number of values of spl rho and ways to remedy this are suggested finally the most effective extrapolation methods for accelerating sommerfeld integral tails are recommended

distributed asynchronous relaxation methods for convex network flow problems we consider the solution of the single commodity strictly convex network flow problem in a distributed asynchronous computation environment the dual of this problem is unconstrained differentiable and well suited for solution via gauss seidel relaxation we show that the structure of the dual allows the successful application of a distributed asynchronous method whereby relaxation iterations are carried out in parallel by several processors in arbitrary order and with arbitrarily large interprocessor communication delays

on the total least squares linear prediction method for frequency estimation the total least squares tls linear prediction lp method recently presented by rahman and yu 1987 and the equivalent improved pisarenko s ip method by kumaresan 1986 are reviewed and generalized by the whitening approach the resulting whitened tls lp method yields higher estimation accuracy than the tls lp this simulation was carried out in double precision fortran 77 on vax 8810 the imsl routines were used to perform eigendecompositions compute the polynomial roots and to generate the pseudo gaussian random numbers

an e relaxation method for separable convex cost generalized network flow problems cover title the extended abstract of this article appeared in the proceedings of the 5th international ipco conference vancouver june 1996 p 1