Work

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

Year: 2025

Type: article

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 $$\ell _1$$ ℓ 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. 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.

Source: Journal of Global Optimization

DOI: 10.1007/s10898-025-01523-3

Authors: Soodeh Habibi, Michal Kočvara, Michael Stingl

Institutions: University of Liverpool, Czech Technical University in Prague, University of Birmingham, Friedrich-Alexander-Universität Erlangen-Nürnberg

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: České Vysoké Učení Technické v Praze, European Commission, Centre National de la Recherche Scientifique