Global error bounds for convex quadratic inequality systems*

Abstract

A global error bound is given for any system of convex quadratic inequalities in terms of a residual function of the system. The residual function consists of the norm of the violation vector plus its l/(2 ^d )-th power, where d is called the degree of singularity of the system. When the system satisfies the Slater constraint qualification, the error bound recovers a result of Luo and Luo [2] with d= 0. The global error bound of Mangasarian and Shiau [10] for monotone linear complementarity problems is also a direct consequence in which d = 1. In general, the degree of singularity is bounded by the number of constraints in the system and the error bound is valid under no constraint qualification on the system. Finally, we show by examples that the error bound is best possible.