Strongly stable C-stationary points for mathematical programs with complementarity constraints

• 成果类型: Article
• 署名作者: Escobar, Daniel Hernandez; Ruckmann, Jan-J
• 署名单位: University of Bergen
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01553-7
• 发表日期: 2021
• 页码: 339-377
• 关键词: optimality conditions; strong stability; tilt stability

摘要

In this paper we consider the class of mathematical programs with complementarity constraints (MPCC). Under an appropriate constraint qualification of Mangasarian-Fromovitz type we present a topological and an equivalent algebraic characterization of a strongly stable C-stationary point for MPCC. Strong stability refers to the local uniqueness, existence and continuous dependence of a solution for each sufficiently small perturbed problem where perturbations up to second order are allowed. This concept of strong stability was originally introduced by Kojima for standard nonlinear optimization; here, its generalization to MPCC demands a sophisticated technique which takes the disjunctive properties of the solution set of MPCC into account.