Aubin Property and Strong Regularity Are Equivalent for Nonlinear Second-Order Cone Programming
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916554538483712 |
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| author | Chen, Liang Chen, Ruoning Sun, Defeng Zhu, Junyuan |
| author_facet | Chen, Liang Chen, Ruoning Sun, Defeng Zhu, Junyuan |
| contents | This paper solves a fundamental open problem in variational analysis on the equivalence between the Aubin property and the strong regularity for nonlinear second-order cone programming (SOCP) at a locally optimal solution. We achieve this by introducing a reduction approach to the Aubin property characterized by the Mordukhovich criterion and a lemma of alternative choices on cones to replace the S-lemma used in Outrata and Ramírez [SIAM J. Optim. 21 (2011) 789-823] and Opazo, Outrata, and Ramírez [SIAM J. Optim. 27 (2017) 2141-2151], where the same SOCP was considered under the strict complementarity condition except for possibly only one block of constraints. As a byproduct, we also offer a new approach to the well-known result of Dontchev and Rockafellar [SIAM J. Optim. 6 (1996) 1087-1105] on the equivalence of the two concepts in conventional nonlinear programming. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13798 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Aubin Property and Strong Regularity Are Equivalent for Nonlinear Second-Order Cone Programming Chen, Liang Chen, Ruoning Sun, Defeng Zhu, Junyuan Optimization and Control 90C, 90C31, 90C46 This paper solves a fundamental open problem in variational analysis on the equivalence between the Aubin property and the strong regularity for nonlinear second-order cone programming (SOCP) at a locally optimal solution. We achieve this by introducing a reduction approach to the Aubin property characterized by the Mordukhovich criterion and a lemma of alternative choices on cones to replace the S-lemma used in Outrata and Ramírez [SIAM J. Optim. 21 (2011) 789-823] and Opazo, Outrata, and Ramírez [SIAM J. Optim. 27 (2017) 2141-2151], where the same SOCP was considered under the strict complementarity condition except for possibly only one block of constraints. As a byproduct, we also offer a new approach to the well-known result of Dontchev and Rockafellar [SIAM J. Optim. 6 (1996) 1087-1105] on the equivalence of the two concepts in conventional nonlinear programming. |
| title | Aubin Property and Strong Regularity Are Equivalent for Nonlinear Second-Order Cone Programming |
| topic | Optimization and Control 90C, 90C31, 90C46 |
| url | https://arxiv.org/abs/2406.13798 |