Verifiable sufficient conditions for the error bound property of second-order cone complementarity problems

• 成果类型: Article
• 署名作者: Ye, Jane J.; Zhou, Jinchuan
• 署名单位: University of Victoria; Shandong University of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1193-9
• 发表日期: 2018
• 页码: 361-395
• 关键词: optimality conditions; mathematical programs; constraint qualifications; optimization problems; disjunctive programs; 1st-order; subregularity

摘要

The error bound property for a solution set defined by a set-valued mapping refers to an inequality that bounds the distance between vectors closed to a solution of the given set by a residual function. The error bound property is a Lipschitz-like/calmness property of the perturbed solution mapping, or equivalently the metric subregularity of the underlining set-valued mapping. It has been proved to be extremely useful in analyzing the convergence of many algorithms for solving optimization problems, as well as serving as a constraint qualification for optimality conditions. In this paper, we study the error bound property for the solution set of a very general second-order cone complementarity problem (SOCCP). We derive some sufficient conditions for error bounds of SOCCP which is verifiable based on the initial problem data.