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

TL;DR

This paper establishes verifiable sufficient conditions for the error bound property in second-order cone complementarity problems, aiding in convergence analysis and optimality conditions in optimization.

Contribution

It introduces new verifiable conditions for the error bound property specific to second-order cone complementarity problems, expanding theoretical understanding.

Findings

Derived verifiable sufficient conditions for error bounds in SOCCP

Conditions depend on initial problem data

Enhances analysis of algorithm convergence and optimality

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.