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Pré-Publication, Document De Travail Année : 2023

Solving Lasserre relaxations of unconstrained binary quadratic optimization problems by an interior-point method

Soodeh Habibi
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Michal Kočvara
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Michael Stingl
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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.
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Dates et versions

hal-04076510 , version 1 (20-04-2023)

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  • HAL Id : hal-04076510 , version 1

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Soodeh Habibi, Michal Kočvara, Michael Stingl. Solving Lasserre relaxations of unconstrained binary quadratic optimization problems by an interior-point method. 2023. ⟨hal-04076510⟩
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