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arXiv · 1706.04723

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

Jane Ye·Jinchuan Zhou
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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.

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Jane Ye, Jinchuan Zhou. 2017-06-15. Verifiable sufficient conditions for the error bound property of second-order cone complementarity problems. https://arxiv.org/abs/1706.04723

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