A finitely convergent circumcenter method for the Convex Feasibility Problem
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916426358456320 |
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| author | Behling, Roger Bello-Cruz, Yunier Iusem, Alfredo Liu, Di Santos, Luiz-Rafael |
| author_facet | Behling, Roger Bello-Cruz, Yunier Iusem, Alfredo Liu, Di Santos, Luiz-Rafael |
| contents | In this paper, we present a variant of the circumcenter method for the Convex Feasibility Problem (CFP), ensuring finite convergence under a Slater assumption. The method replaces exact projections onto the convex sets with projections onto separating halfspaces, perturbed by positive exogenous parameters that decrease to zero along the iterations. If the perturbation parameters decrease slowly enough, such as the terms of a diverging series, finite convergence is achieved. To the best of our knowledge, this is the first circumcenter method for CFP that guarantees finite convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09849 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A finitely convergent circumcenter method for the Convex Feasibility Problem Behling, Roger Bello-Cruz, Yunier Iusem, Alfredo Liu, Di Santos, Luiz-Rafael Optimization and Control 49M27, 65K05, 65B99, 90C25 In this paper, we present a variant of the circumcenter method for the Convex Feasibility Problem (CFP), ensuring finite convergence under a Slater assumption. The method replaces exact projections onto the convex sets with projections onto separating halfspaces, perturbed by positive exogenous parameters that decrease to zero along the iterations. If the perturbation parameters decrease slowly enough, such as the terms of a diverging series, finite convergence is achieved. To the best of our knowledge, this is the first circumcenter method for CFP that guarantees finite convergence. |
| title | A finitely convergent circumcenter method for the Convex Feasibility Problem |
| topic | Optimization and Control 49M27, 65K05, 65B99, 90C25 |
| url | https://arxiv.org/abs/2308.09849 |