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Fixing Variables in Semidefinite Relaxations (1996)
| Venue: | SIAM J. MATRIX ANAL. APPL |
| Citations: | 27 - 2 self |
BibTeX
@ARTICLE{Helmberg96fixingvariables,
author = {Christoph Helmberg},
title = {Fixing Variables in Semidefinite Relaxations},
journal = {SIAM J. MATRIX ANAL. APPL},
year = {1996},
volume = {21},
pages = {2000}
}
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Abstract
The standard technique of reduced cost fixing from linear programming is not trivially extensible to semidefinite relaxations as the corresponding Lagrange multipliers are usually not available. We propose a general technique for computing reasonable Lagrange multipliers to constraints which are not part of the problem description. Its specialization to the semidefinite f\Gamma1; 1g relaxation of quadratic 0-1 programming yields an efficient routine for fixing variables. The routine offers the possibility to exploit problem structure. We extend the traditional bijective map between f0; 1g and f\Gamma1; 1g formulations to the constraints such that the dual variables remain the same and structural properties are preserved. In consequence the fixing routine can efficiently be applied to optimal solutions of the semidefinite f0; 1g relaxation of constrained quadratic 0-1 programming, as well. We provide numerical results showing the efficacy of the approach.
Keyphrases
semidefinite relaxation problem description quadratic 0-1 programming yield problem structure reasonable lagrange multiplier optimal solution numerical result linear programming general technique efficient routine reduced cost fixing corresponding lagrange multiplier structural property semidefinite gamma1 quadratic 0-1 programming semidefinite f0 traditional bijective map dual variable standard technique
