Lipschitz and Holder stability of optimization problems and generalized equations

• 成果类型: Article
• 署名作者: Gfrerer, Helmut; Klatte, Diethard
• 署名单位: Johannes Kepler University Linz; University of Zurich
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0914-1
• 发表日期: 2016
• 页码: 35-75
• 关键词: nonsmooth mathematical programs; 2nd-order optimality conditions; constraint qualifications; vanishing constraints; complementarity constraints; metric subregularity; stationary points; sensitivity; calmness; MULTIFUNCTIONS

摘要

This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications ensuring metric subregularity of the constraint mapping, continuity results of upper Lipschitz and upper Holder type, respectively, hold. Furthermore, we apply the above results to parametric mathematical programs with equilibrium constraints and demonstrate, how some classical results for the nonlinear programming problem can be recovered and even improved by our theory.