Characterizations of the Aubin property of the solution mapping for nonlinear semidefinite programming

• 成果类型: Article; Early Access
• 署名作者: Chen, Liang; Chen, Ruoning; Sun, Defeng; Zhang, Liping
• 署名单位: Hunan University; Tsinghua University; Hong Kong Polytechnic University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-025-02231-2
• 发表日期: 2025
• 关键词: constraint nondegeneracy; variational-inequalities; generalized equations; STABILITY; sensitivity; REGULARITY

摘要

In this paper, we study the Aubin property of the Karush-Kuhn-Tucker solution mapping for the nonlinear semidefinite programming (NLSDP) problem at a locally optimal solution. In the literature, it is known that the Aubin property implies the constraint nondegeneracy by Fusek (SIAM J. Optim. 23:1041-1061, 2013) and the second-order sufficient condition by Ding et al. (SIAM J. Optim. 27:67-90, 2017). Based on the Mordukhovich criterion, here we further prove that the strong second-order sufficient condition is also necessary for the Aubin property to hold. Consequently, several equivalent conditions including the strong regularity are established for NLSDP's Aubin property. Together with the recent progress made by Chen et al. (SIAM J. Optim. 35:712-738, 2025) on the equivalence between the Aubin property and the strong regularity for nonlinear second-order cone programming, this paper constitutes a significant step forward in characterizing the Aubin property for general non-polyhedral C2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>2$$\end{document}-cone reducible constrained optimization problems.