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Using continuous nonlinear relaxations to solve. constrained maximum-entropy sampling problems

Using continuous nonlinear relaxations to solve. constrained maximum-entropy sampling problems Math. Program. 85: 221–240 (1999) © Springer-Verlag 1999 Digital Object Identifier (DOI) 10.1007/s10107980041a Kurt M. Anstreicher Marcia Fampa Jon Lee Joy Williams Using continuous nonlinear relaxations to solve constrained maximum-entropy sampling problems Received January 9, 1997 / Revised version received January 26, 1998 Published online November 24, 1998 Abstract. We consider a new nonlinear relaxation for the Constrained Maximum-Entropy Sampling Problem – the problem of choosing the s s principal submatrix with maximal determinant from a given n n positive definite matrix, subject to linear constraints. We implement a branch-and-bound algorithm for the problem, using the new relaxation. The performance on test problems is far superior to a previous implementation using an eigenvalue-based relaxation. A parallel implementation of the algorithm exhibits approximately linear speed-up for up to 8 processors, and has successfully solved problem instances that were heretofore intractable. Key words. maximum-entropy sampling – branch and bound – nonlinear programming 1. Introduction Let n be a positive integer. For N VD f1;::: ; ng,let Y VD fY j j 2 Ng beaset of N j n random variables, with joint-density function g ./.Let s be an integer satisfying 0 < s  n.For S  N, jSjD s,let Y http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Programming Springer Journals

Using continuous nonlinear relaxations to solve. constrained maximum-entropy sampling problems

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References (25)

Publisher
Springer Journals
Copyright
Copyright © 1999 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Mathematics of Computing; Numerical Analysis; Combinatorics; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics
ISSN
0025-5610
eISSN
1436-4646
DOI
10.1007/s101070050055
Publisher site
See Article on Publisher Site

Abstract

Math. Program. 85: 221–240 (1999) © Springer-Verlag 1999 Digital Object Identifier (DOI) 10.1007/s10107980041a Kurt M. Anstreicher Marcia Fampa Jon Lee Joy Williams Using continuous nonlinear relaxations to solve constrained maximum-entropy sampling problems Received January 9, 1997 / Revised version received January 26, 1998 Published online November 24, 1998 Abstract. We consider a new nonlinear relaxation for the Constrained Maximum-Entropy Sampling Problem – the problem of choosing the s s principal submatrix with maximal determinant from a given n n positive definite matrix, subject to linear constraints. We implement a branch-and-bound algorithm for the problem, using the new relaxation. The performance on test problems is far superior to a previous implementation using an eigenvalue-based relaxation. A parallel implementation of the algorithm exhibits approximately linear speed-up for up to 8 processors, and has successfully solved problem instances that were heretofore intractable. Key words. maximum-entropy sampling – branch and bound – nonlinear programming 1. Introduction Let n be a positive integer. For N VD f1;::: ; ng,let Y VD fY j j 2 Ng beaset of N j n random variables, with joint-density function g ./.Let s be an integer satisfying 0 < s  n.For S  N, jSjD s,let Y

Journal

Mathematical Programming – Springer Journals

Published: Jun 1, 1999

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