Error bound results for convex inequality systems via conjugate duality

Details Error bound results for convex inequality systems via conjugate duality Error bound results for convex inequality systems via conjugate duality

2010-07-11

arxiv.org/abs/1007.1776v1

Mathematics

Optimization and Control

12 pages

Scientific paper

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.

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