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Handbook of semidefinite programming
"... Semidefinite programming (or SDP) has been one of the most exciting and active research areas in optimization during the 1990s. It has attracted researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, con ..."
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Cited by 89 (3 self)
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Semidefinite programming (or SDP) has been one of the most exciting and active research areas in optimization during the 1990s. It has attracted researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This tremendous research activity was spurred by the discovery of important applications in combinatorial optimization and control theory, the development of efficient interiorpoint algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory. This book includes nineteen chapters on the theory, algorithms, and applications of semidefinite programming. Written by the leading experts on the subject, it offers an advanced and broad overview of the current state of the field. The coverage is somewhat less comprehensive, and the overall level more advanced, than we had planned at the start of the project. In order to finish the book in a timely fashion, we have had to abandon hopes for separate chapters on some important topics (such as a discussion of SDP algorithms in the
An Enabling Framework for MasterWorker Applications on the Computational Grid
 Cluster Computing
, 2000
"... We describe MW  a software framework that allows users to quickly and easily parallelize scientific computations using the masterworker paradigm on the computational grid. MW provides both a "top level" interface to application software and a "bottom level" interface to exi ..."
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Cited by 82 (9 self)
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We describe MW  a software framework that allows users to quickly and easily parallelize scientific computations using the masterworker paradigm on the computational grid. MW provides both a "top level" interface to application software and a "bottom level" interface to existing grid computing toolkits. Both interfaces are briefly described. We conclude with a case study, where the necessary Grid services are provided by the Condor highthroughput computing system, and the MWenabled application code is used to solve a combinatorial optimization problem of unprecedented complexity. This work was supported in part by Grants No. CDA9726385 and CDA9623632 from the National Science Foundation. y Department of Electrical and Computer Engineering, Northwestern University, and Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, goux@mcs.anl.gov z Computer Sciences Department, University of Wisconsin  Madison, 1210 West Dayton Street, Madison, WI 53706, fsanjeevk,yodermeg@cs.wisc.edu x Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, linderot@mcs.anl.gov 1 1
Solving Large Quadratic Assignment Problems on Computational Grids
, 2000
"... The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Some instances of size n = 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computat ..."
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Cited by 82 (7 self)
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The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Some instances of size n = 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computational platforms. In this article we describe a novel approach to solve QAPs using a stateoftheart branchandbound algorithm running on a federation of geographically distributed resources known as a computational grid. Solution of QAPs of unprecedented complexity, including the nug30, kra30b, and tho30 instances, is reported.
A path following algorithm for the graph matching problem
, 2009
"... We propose a convexconcave programming approach for the labeled weighted graph matching problem. The convexconcave programming formulation is obtained by rewriting the weighted graph matching problem as a leastsquare problem on the set of permutation matrices and relaxing it to two different opti ..."
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Cited by 43 (4 self)
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We propose a convexconcave programming approach for the labeled weighted graph matching problem. The convexconcave programming formulation is obtained by rewriting the weighted graph matching problem as a leastsquare problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convexconcave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.
Metacomputing and the MasterWorker Paradigm
 PREPRINT MCS/ANLP7920200, MATHEMATICS AND COMPUTER SCIENCE DIVISION, ARGONNE NATIONAL LABORATORY, ARGONNE
, 2000
"... The goal of our work is to create a tool that easily allows users to distribute large scientific computations in metacomputing environments. To achieve this goal, a number of difficult implementation issues must be addressed, which may explain the relative lack of complete tools addressing this purp ..."
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Cited by 32 (8 self)
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The goal of our work is to create a tool that easily allows users to distribute large scientific computations in metacomputing environments. To achieve this goal, a number of difficult implementation issues must be addressed, which may explain the relative lack of complete tools addressing this purpose. Our tool relies on the simple master worker paradigm, and we show that this paradigm is nicely suited for performing many of the requisite tasks of our metacomputing tool. We describe an implementation and present a case study showing the paradigm's effectiveness in solving large scientific computing problems.
Solving Quadratic Assignment Problems Using Convex Quadratic Programming Relaxations
, 2000
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Tree Elaboration Strategies In Branch and Bound Algorithms For Solving the Quadratic Assignment Problem
, 1999
"... This paper presents a new strategy for selecting nodes in a branchandbound algorithm for solving exactly the Quadratic Assignment Problem (QAP). It was developed when it was learned that older strategies failed on the larger size problems. The strategy is a variation of polytomic depthfirst searc ..."
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Cited by 12 (3 self)
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This paper presents a new strategy for selecting nodes in a branchandbound algorithm for solving exactly the Quadratic Assignment Problem (QAP). It was developed when it was learned that older strategies failed on the larger size problems. The strategy is a variation of polytomic depthfirst search of Mautor and Roucairol which extends a node by all assignments of an unassigned facility to unassigned locations based upon the counting of 'forbidden' locations. A forbidden location is one where the addition of the corresponding leader (linear cost) element would increase the lower bound beyond the upper bound. We learned that this fortuitous situation never occurs near the root on Nugent problems larger than 15. One has to make better estimates of the bound if the strategy is to work. We have, therefore, designed and implemented an increasingly improved set of bound calculations. The better of these bound calculations to be utilized near the root and the less accurate (poorer bounds) utilized further into the tree. The result is an effective and powerful technique for shortening the run times of problem instances in the range of size 16 to 25. Run times were decreased generally by five or sixtoone and the number of nodes evaluated was decreased as much as 10toone. Later improvements in our strategy produced a better than 3to1 reduction in runtime so that overall improvement in run time was as high as 20to1 as compared to our earlier results. At the end of our paper, we compare the performance of the four most successful algorithms for exact solution of the QAP.
Estimating Bounds for Quadratic Assignment Problems Associated with Hamming and Manhattan Distance Matrices based on Semidefinite Programming
, 2008
"... Quadratic assignment problems (QAPs) with a Hamming distance matrix for a hypercube or a Manhattan distance matrix for a rectangular grid arise frequently from communications and facility locations and are known to be among the hardest discrete optimization problems. In this paper we consider the is ..."
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Cited by 10 (4 self)
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Quadratic assignment problems (QAPs) with a Hamming distance matrix for a hypercube or a Manhattan distance matrix for a rectangular grid arise frequently from communications and facility locations and are known to be among the hardest discrete optimization problems. In this paper we consider the issue of how to obtain lower bounds for those two classes of QAPs based on semidefinite programming (SDP). By exploiting the data structure of the distance matrix B, we first show that for any permutation matrix X, the matrix Y = αE − XBX T is positive semidefinite, where α is a properly chosen parameter depending only on the associated graph in the underlying QAP and E = ee T is a rank one matrix whose elements have value 1. This results in a natural way to approximate the original QAPs via SDP relaxation based on the matrix splitting technique. Our new SDP relaxations have a smaller size compared with other SDP relaxations in the literature and can be solved efficiently by most open source SDP solvers. Experimental results show that for the underlying QAPs of size up to n=200, strong bounds can be obtained effectively.
A Level3 ReformulationLinearization Technique Based Bound for the Quadratic Assignment Problem
"... We apply the level3 Reformulation Linearization Technique (RLT3) to the Quadratic Assignment Problem (QAP). We then present our experience in calculating lower bounds using an essentially new algorithm, based on this RLT3 formulation. This algorithm is not guaranteed to calculate the RLT3 lower bou ..."
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Cited by 9 (1 self)
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We apply the level3 Reformulation Linearization Technique (RLT3) to the Quadratic Assignment Problem (QAP). We then present our experience in calculating lower bounds using an essentially new algorithm, based on this RLT3 formulation. This algorithm is not guaranteed to calculate the RLT3 lower bound exactly, but approximates it very closely and reaches it in some instances. For Nugent problem instances up to size 24, our RLT3based lower bound calculation solves these problem instances exactly or serves to verify the optimal value. Calculating lower bounds for problems sizes larger than size 25 still presents a challenge due to the large memory needed to implement the RLT3 formulation. Our presentation emphasizes the steps taken to significantly conserve memory by using the numerous problem symmetries in the RLT3 formulation of the QAP.