Verifiable sufficient conditions for the error bound property of second-order cone complementarity problems
Abstract
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.
Cite
@article{arxiv.1706.04723,
title = {Verifiable sufficient conditions for the error bound property of second-order cone complementarity problems},
author = {Jane Ye and Jinchuan Zhou},
journal= {arXiv preprint arXiv:1706.04723},
year = {2017}
}