Aubin Property and Strong Regularity Are Equivalent for Nonlinear Second-Order Cone Programming
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.
Cite
@article{arxiv.2406.13798,
title = {Aubin Property and Strong Regularity Are Equivalent for Nonlinear Second-Order Cone Programming},
author = {Liang Chen and Ruoning Chen and Defeng Sun and Junyuan Zhu},
journal= {arXiv preprint arXiv:2406.13798},
year = {2025}
}
Comments
To appear in SIAM Journal on Optimization