A Lipschitzian Error Bound for Convex Quadratic Symmetric Cone Programming

Abstract

Under a Slater-type condition, we reformulate a convex quadratic symmetric cone programming problem as an unconstrained eigenvalue minimization problem, and obtain a sufficient condition ensuring the existence of a Lipschitzian error bound for the eigenvalue minimization problem. This error bound, in turn, provides an estimation of the distance from a feasible solution of the convex quadratic symmetric cone program to its optimal solution set.