Error bound results for convex inequality systems via conjugate duality

TL;DR

This paper develops new conjugate duality-based techniques to establish global error bounds for convex inequality systems, extending classical results and providing sharper conditions for vector inequalities.

Contribution

It introduces novel methods using conjugate duality to prove error bounds for convex inequalities, including vector systems, improving upon existing results.

Findings

Established new error bound results for convex inequalities using conjugate duality.

Extended scalar inequality results to vector inequality systems.

Sharpened classical error bound conditions of Robinson.

Abstract

The aim of this paper is to implement some new techniques, based on conjugate duality in convex optimization, for proving the existence of global error bounds for convex inequality systems. We deal first of all with systems described via one convex inequality and extend the achieved results, by making use of a celebrated scalarization function, to convex inequality systems expressed by means of a general vector function. We also propose a second approach for guaranteeing the existence of global error bounds of the latter, which meanwhile sharpens the classical result of Robinson.