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Stability of error bounds for semi-infinite convex constraint systems

Huynh Van Ngai (nghiakhiem***at***yahoo.com)
Alexander Y. Kruger (a.kruger***at***ballarat.edu.au)
Michel Th\'era (michel.thera***at***unilim.fr)

Abstract: In this paper, we are concerned with the stability of the error bounds for semi-infinite convex constraint systems. Roughly speaking, the error bound of a system of inequalities is said to be stable if all its "small" perturbations admit a (local or global) error bound. We first establish subdifferential characterizations of the stability of error bounds for semi-infinite systems of convex inequalities. By applying these characterizations, we extend some results established by Az\'e and Corvellec on the sensitivity analysis of Hoffman constants to semi-infinite linear constraint systems.

Keywords: error bounds, Hoffman constants, subdifferential

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Published in SIAM Journal on Optimization 20 (2010), no. 4, 2080-2096. The original publication is available at http://link.aip.org/link/?SJE/20/2080

Download: [PDF]

Entry Submitted: 08/16/2009
Entry Accepted: 08/16/2009
Entry Last Modified: 05/23/2010

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