On the Approximation of Unbounded Convex Sets by Polyhedra
| Autor: | Dörfler, Daniel |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Journal of Optimization Theory and Applications 194, 265-287 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10957-022-02020-3 |
| Popis: | This article is concerned with the approximation of unbounded convex sets by polyhedra. While there is an abundance of literature investigating this task for compact sets, results on the unbounded case are scarce. We first point out the connections between existing results before introducing a new notion of polyhedral approximation called ($\varepsilon,\delta$)-approximation that integrates the unbounded case in a meaningful way. Some basic results about ($\varepsilon,\delta$)- approximations are proven for general convex sets. In the last section an algorithm for the computation of ($\varepsilon,\delta$)-approximations of spectrahedra is presented. Correctness and finiteness of the algorithm are proven. Comment: 22 pages, 4 figures, 1 table; correction of Algorithm 2, added Proposition 5.5, added references |
| Databáze: | arXiv |
| Externí odkaz: |
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