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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2210.11252 |
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| _version_ | 1866929306678067200 |
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| author | Bui, Hoa T. Burachik, Regina S. Nurminski, Evgeni A. Tam, Matthew K. |
| author_facet | Bui, Hoa T. Burachik, Regina S. Nurminski, Evgeni A. Tam, Matthew K. |
| contents | In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those established for the linear programming setting in Nurminski (2015) by considering problems that: (i) may have multiple solutions, (ii) do not satisfy strict complementary conditions, and (iii) possess non-linear convex constraints. As a by-product of our analysis, we provide a quantitative estimate on the required distance between the infeasible point and the feasible set in order for its projection to be a solution of the problem. Our analysis relies on a "sharpness" property of the constraint set; a new property we introduce here. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_11252 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Single-Projection Procedure for Infinite Dimensional Convex Optimization Problems Bui, Hoa T. Burachik, Regina S. Nurminski, Evgeni A. Tam, Matthew K. Optimization and Control In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those established for the linear programming setting in Nurminski (2015) by considering problems that: (i) may have multiple solutions, (ii) do not satisfy strict complementary conditions, and (iii) possess non-linear convex constraints. As a by-product of our analysis, we provide a quantitative estimate on the required distance between the infeasible point and the feasible set in order for its projection to be a solution of the problem. Our analysis relies on a "sharpness" property of the constraint set; a new property we introduce here. |
| title | Single-Projection Procedure for Infinite Dimensional Convex Optimization Problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2210.11252 |