Solving Lasserre relaxations of unconstrained binary quadratic optimization problems by an interior-point method
Résumé
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate gradient method solving the linear systems. The preconditioner utilizes the low-rank structure of the solution of the relaxations. In order to fully exploit this, we need to rewrite the moment relaxations. To treat the arising linear equality constraints we use an 1-penalty approach within the interior-point solver. The efficiency of this approach is demonstrated by numerical experiments with the MAXCUT and other randomly generated problems and a comparison with a state-of-the-art semidefinite solver and the ADMM method. As a by-product, we observe that the second-order relaxation is often high enough to deliver a globally optimal solution of the original problem.
Mots clés
Binary quadratic optimization Lasserre hierarchy semidefinite optimization interior-point methods preconditioned conjugate gradients MAXCUT problem MSC Classification: 90C22 90C51 65F08 74P05
Binary quadratic optimization
Lasserre hierarchy
semidefinite optimization
interior-point methods
preconditioned conjugate gradients
MAXCUT problem MSC Classification: 90C22
90C51
65F08
74P05
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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