On the numerical solution of Lasserre relaxations of unconstrained binary quadratic optimization problem

Habibi S, Kočvara M, Stingl M (2025)


Publication Type: Journal article

Publication year: 2025

Journal

DOI: 10.1007/s10898-025-01523-3

Abstract

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 re-write the moment relaxations. To treat the arising linear equality constraints we use an ℓ1-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. We further propose a hybrid ADMM-interior-point method that proves to be efficient for certain problem classes. 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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APA:

Habibi, S., Kočvara, M., & Stingl, M. (2025). On the numerical solution of Lasserre relaxations of unconstrained binary quadratic optimization problem. Journal of Global Optimization. https://doi.org/10.1007/s10898-025-01523-3

MLA:

Habibi, Soodeh, Michal Kočvara, and Michael Stingl. "On the numerical solution of Lasserre relaxations of unconstrained binary quadratic optimization problem." Journal of Global Optimization (2025).

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