Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/330636 
Erscheinungsjahr: 
2025
Quellenangabe: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 93 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2025 [Pages:] 63-85
Verlag: 
Springer US, New York, NY
Zusammenfassung: 
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.
Schlagwörter: 
Binary quadratic optimization
Lasserre hierarchy
Semidefinite optimization
Interior-point methods
Preconditioned conjugate gradients
MAXCUT problem
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