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Adaptive Use Of Iterative Methods In Interior Point Methods For Linear Programming
, 1995
"... In this work we devise efficient algorithms for finding the search directions for interior point methods applied to linear programming problems. There are two innovations. The first is the use of updating of preconditioners computed for previous barrier parameters. The second is an adaptive automate ..."
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Cited by 15 (3 self)
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In this work we devise efficient algorithms for finding the search directions for interior point methods applied to linear programming problems. There are two innovations. The first is the use of updating of preconditioners computed for previous barrier parameters. The second is an adaptive automated procedure for determining whether to use a direct or iterative solver, whether to reinitialize or update the preconditioner, and how many updates to apply. These decisions are based on predictions of the cost of using the different solvers to determine the next search direction, given costs in determining earlier directions. These ideas are tested by applying a modified version of the OB1R code of Lustig, Marsten, and Shanno to a variety of problems from the NETLIB and other collections. If a direct method is appropriate for the problem, then our procedure chooses it, but when an iterative procedure is helpful, substantial gains in efficiency can be obtained.
Techniques for Traffic Engineering of Multiservice, Multipriority Networks
 Bell Labs Technical Journal
, 2001
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A Branch and Bound Algorithm for the Quadratic Assignment Problem using a Lower Bound Based on Linear Programming
 In C. Floudas and P.M. Pardalos, editors, State of the Art in Global Optimization: Computational Methods and Applications
, 1995
"... In this paper, we study a branch and bound algorithm for the quadratic assignment problem (QAP) that uses a lower bound based on the linear programming (LP) relaxation of a classical integer programming formulation of the QAP. Computational experience with the branch and bound algorithm on several Q ..."
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Cited by 10 (2 self)
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In this paper, we study a branch and bound algorithm for the quadratic assignment problem (QAP) that uses a lower bound based on the linear programming (LP) relaxation of a classical integer programming formulation of the QAP. Computational experience with the branch and bound algorithm on several QAP test problems is reported. The linear programming relaxations are solved with an implementation of an interior point algorithm that uses a preconditioned conjugate gradient algorithm to compute directions. The branch and bound algorithm is compared with a similar branch and bound algorithm that uses the GilmoreLawler lower bound (GLB) instead of the LPbased bound. The LPbased algorithm examines a small portion of the nodes explored by the GLBbased algorithm. 1 Introduction The quadratic assignment problem (QAP), first proposed by Koopmans and Beckmann [16], can be stated as min p2\Pi n X i=1 n X j=1 a ij b p(i)p(j) ; To appear in Proceedings of State of the Art in Global Opti...
Interior Point Algorithms For Network Flow Problems
 in Advances in linear and integer programming
, 1996
"... . Computational algorithms for the solution of network flow problems are of great practical significance. In the last decade, a new class of computationally efficient algorithms, based on the interior point method, has been proposed and applied to solve large scale network flow problems. In this cha ..."
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Cited by 10 (2 self)
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. Computational algorithms for the solution of network flow problems are of great practical significance. In the last decade, a new class of computationally efficient algorithms, based on the interior point method, has been proposed and applied to solve large scale network flow problems. In this chapter, we review interior point approaches for network flows, with emphasis on computational issues. Key words. Network flow problems, interior point methods, computational testing, computer implementation. AMS(MOS) subject classifications. 90B10, 90C05, 90C06, 90C35, 6505, 65F10, 65F50 1. Introduction. A large number of problems in transportation, communications, and manufacturing can be modeled as network flow problems. In these problems one seeks to find the most efficient, or optimal, way to move flow (e.g. materials, information, buses, electrical currents) on a network (e.g. postal network, computer network, transportation grid, power grid). Among these optimization problems, many a...
Computational and Complexity Results for an Interior Point Algorithm on Multicommodity Flow Problems (Extended Abstract)
 In Netflow
, 1994
"... 1 Introduction In this paper, we present some computational and complexity results for an Approximate Dual Projective (ADP) variant of the interior point algorithm [9] for solving the minimum cost Multicommodity Network Flow Problem (MCNF). The motivation for this work is to study the performance o ..."
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1 Introduction In this paper, we present some computational and complexity results for an Approximate Dual Projective (ADP) variant of the interior point algorithm [9] for solving the minimum cost Multicommodity Network Flow Problem (MCNF). The motivation for this work is to study the performance of the ADP algorithm for solving a special class of LPs arising in MCNF. In MCNF, there are k commodities and k sourcesink pairs (s i ; t i ). The problem is to simultaneously transport, at minimum total cost, d i units of the i th commodity from s i to t i subject to the constraint that the total flow of the commodities through each edge is bounded by capacity u(e) of the edge. Formally, an instance of the problem consists of a directed graph G = (V; E), and a set of commodities K. For each commodity i 2 K we are given a sourcesink pair (s i ; t i ) 2 V \Theta V and a demand d i 2 R. Each edge e 2 E has a capacity u(e) and costs c (i) (e) for each commodity i 2 K. A multicommodity flo...
Identifying The Optimal Face Of A Network Linear Program With A Globally Convergent Interior Point Method
 in Large scale optimization: State of the
, 1994
"... . Based on recent convergence results for the affine scaling algorithm for linear programming, we investigate strategies to identify the optimal face of a minimum cost network flow problem. In the computational experiments described, one of the proposed optimality indicators is used to implement an ..."
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Cited by 9 (3 self)
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. Based on recent convergence results for the affine scaling algorithm for linear programming, we investigate strategies to identify the optimal face of a minimum cost network flow problem. In the computational experiments described, one of the proposed optimality indicators is used to implement an early stopping criterion in dlnet, an implementation of the dual affine scaling algorithm for solving minimum cost network flow problems. We conclude from the experiments that the new indicator is far more robust than the one used in earlier versions of dlnet. Key words. Linear programming, minimum cost network flow, indicator, affine scaling algorithm, computer implementation. AMS(MOS) subject classifications. 6505, 65F10, 65K05, 65Y05, 90C05, 90C06, 90C35 1. Introduction. The dual affine scaling (das) algorithm [3] has been shown to perform well in practice on linear programming problems [1, 2, 7, 8], largescale network flow problems [13], and largescale assignment problems [11, 12]. ...
ON MUTUAL IMPACT OF NUMERICAL LINEAR ALGEBRA AND LARGESCALE OPTIMIZATION WITH FOCUS ON INTERIOR POINT METHODS
, 2008
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Large Scale Unconstrained Optimization
 The State of the Art in Numerical Analysis
, 1996
"... This paper reviews advances in Newton, quasiNewton and conjugate gradient methods for large scale optimization. It also describes several packages developed during the last ten years, and illustrates their performance on some practical problems. Much attention is given to the concept of partial ..."
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Cited by 8 (0 self)
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This paper reviews advances in Newton, quasiNewton and conjugate gradient methods for large scale optimization. It also describes several packages developed during the last ten years, and illustrates their performance on some practical problems. Much attention is given to the concept of partial separabilitywhich is gaining importance with the arrival of automatic differentiation tools and of optimization software that fully exploits its properties.
Optimal Design of Signaling Networks for Internet Telephony
, 2000
"... We present an approach for efficient design of a signaling network for a network of software switches supporting Internet telephony. While one may take an Integer Programming approach to solve this problem, it quickly becomes intractable even for modestsized networks. Instead, our topology design u ..."
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Cited by 7 (0 self)
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We present an approach for efficient design of a signaling network for a network of software switches supporting Internet telephony. While one may take an Integer Programming approach to solve this problem, it quickly becomes intractable even for modestsized networks. Instead, our topology design uses random graphs that we show to be nearly optimal in cost, highly connected, and computationally efficient even for large networks. (Prior work [4] has addressed topology design using random graph techniques. We identified some gaps in this work, for which we provide resolutions.) We then formulate a Quadratic Assignment Problem (QAP) to map the abstract topology into the physical network to achieve optimal load balancing for given demand forecasts, which we solve using randomized heuristics. Numerical results on several example networks illustrate the performance and computational efficiency of our method. A graphical design tool has been developed based on our algorithms. I. INTRODUCTION...
Global Optimization Problems in Computer Vision
 In C.A. Floudas and P.M. Pardalos, editors, State of the Art in Global Optimization
, 1995
"... In the field of computer vision, computer scientists extract knowledge from an image by manipulating it through image transforms. In the mathematical language of image algebra an image transformation often CO1Tesponds to an imagetemplate product. When performing this operation on a computer, saving ..."
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Cited by 5 (3 self)
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In the field of computer vision, computer scientists extract knowledge from an image by manipulating it through image transforms. In the mathematical language of image algebra an image transformation often CO1Tesponds to an imagetemplate product. When performing this operation on a computer, savings in time and memory as well as a better fit to the specific computer architecture can often be achieved by using the technique of template decomposition. In this paper we use global optimization techniques to solve a general problem of morphological template decomposition.