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arXiv · 2406.13798

Aubin Property and Strong Regularity Are Equivalent for Nonlinear Second-Order Cone Programming

Liang Chen·Ruoning Chen·Defeng Sun·Junyuan Zhu
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Abstract

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 Ram\'irez [SIAM J. Optim. 21 (2011) 789-823] and Opazo, Outrata, and Ram\'irez [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.

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Liang Chen, Ruoning Chen, Defeng Sun, Junyuan Zhu. 2024-06-19. Aubin Property and Strong Regularity Are Equivalent for Nonlinear Second-Order Cone Programming. https://arxiv.org/abs/2406.13798

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