| Autor: |
Habibi, Soodeh, Kocvara, Michal, Stingl, Michael |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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 $\ell_1$-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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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