Second-Order Optimality Conditions for Nonconvex Set-Constrained Optimization Problems

• 成果类型: Article; Early Access
• 署名作者: Gfrerer, Helmut; Ye, Jane J.; Zhou, Jinchuan
• 署名单位: Johannes Kepler University Linz; University of Victoria; Shandong University of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1211
• 发表日期: 2022
• 关键词: mathematical programs; Sufficient conditions; disjunctive programs; subregularity; stationarity; REGULARITY; 1st-order; calmness

摘要

In this paper, we study second-order optimality conditions for nonconvex setconstrained optimization problems. For a convex set-constrained optimization problem, it is well known that second-order optimality conditions involve the support function of the second-order tangent set. In this paper, we propose two approaches for establishing second-order optimality conditions for the nonconvex case. In the first approach, we extend the concept of the support function so that it is applicable to general nonconvex setconstrained problems, whereas in the second approach, we introduce the notion of the directional regular tangent cone and apply classical results of convex duality theory. Besides the second-order optimality conditions, the novelty of our approach lies in the systematic introduction and use, respectively, of directional versions of well-known concepts from variational analysis.