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Correlative Sparsity in Primal-Dual Interior-Point Methods for LP, SDP, and SOCP

Correlative Sparsity in Primal-Dual Interior-Point Methods for LP, SDP, and SOCP Exploiting sparsity has been a key issue in solving large-scale optimization problems. The most time-consuming part of primal-dual interior-point methods for linear programs, second-order cone programs, and semidefinite programs is solving the Schur complement equation at each iteration, usually by the Cholesky factorization. The computational efficiency is greatly affected by the sparsity of the coefficient matrix of the equation which is determined by the sparsity of an optimization problem (linear program, semidefinite program or second-order cone program). We show if an optimization problem is correlatively sparse , then the coefficient matrix of the Schur complement equation inherits the sparsity, and a sparse Cholesky factorization applied to the matrix results in no fill-in. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Correlative Sparsity in Primal-Dual Interior-Point Methods for LP, SDP, and SOCP

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References (38)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer Science+Business Media, LLC
Subject
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-007-9030-9
Publisher site
See Article on Publisher Site

Abstract

Exploiting sparsity has been a key issue in solving large-scale optimization problems. The most time-consuming part of primal-dual interior-point methods for linear programs, second-order cone programs, and semidefinite programs is solving the Schur complement equation at each iteration, usually by the Cholesky factorization. The computational efficiency is greatly affected by the sparsity of the coefficient matrix of the equation which is determined by the sparsity of an optimization problem (linear program, semidefinite program or second-order cone program). We show if an optimization problem is correlatively sparse , then the coefficient matrix of the Schur complement equation inherits the sparsity, and a sparse Cholesky factorization applied to the matrix results in no fill-in.

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Aug 1, 2008

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