2017/06/15 by Jane J. Ye, Ye, Jane, Jinchuan Zhou +1 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1706.04723
openalex publication_date 2017/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 for SOCCP which is verifiable based on the initial problem data.