Accelerating MPGP-type Methods Through Preconditioning
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911693320224768 |
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| author | Kružík, Jakub Horák, David |
| author_facet | Kružík, Jakub Horák, David |
| contents | This work investigates the acceleration of MPGP-type algorithms using preconditioning for the solution of quadratic programming problems. The preconditioning needs to be done only on the free set so as not to change the constraints. A variant of preconditioning restricted to the free set is the preconditioning in face. The inner preconditioner in preconditioning in face needs to be recomputed or updated every time the free set changes. Here, we investigate an approximate variant of preconditioning in face that computes the inner preconditioner only once. We analyze the error of the approximate variant, give a sharp bound on the condition number of the preconditioned operator, and provide numerical experiments demonstrating that very large speedups can be achieved by the approximate variant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00617 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accelerating MPGP-type Methods Through Preconditioning Kružík, Jakub Horák, David Numerical Analysis Optimization and Control 47N10, 65K10 G.1.6 This work investigates the acceleration of MPGP-type algorithms using preconditioning for the solution of quadratic programming problems. The preconditioning needs to be done only on the free set so as not to change the constraints. A variant of preconditioning restricted to the free set is the preconditioning in face. The inner preconditioner in preconditioning in face needs to be recomputed or updated every time the free set changes. Here, we investigate an approximate variant of preconditioning in face that computes the inner preconditioner only once. We analyze the error of the approximate variant, give a sharp bound on the condition number of the preconditioned operator, and provide numerical experiments demonstrating that very large speedups can be achieved by the approximate variant. |
| title | Accelerating MPGP-type Methods Through Preconditioning |
| topic | Numerical Analysis Optimization and Control 47N10, 65K10 G.1.6 |
| url | https://arxiv.org/abs/2507.00617 |