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Stability of error bounds for convex constraint systems in Banach spaces

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

Abstract: This paper studies stability of error bounds for convex constraint systems in Banach spaces. We show that certain known sufficient conditions for local and global error bounds actually ensure error bounds for the family of functions being in a sense small perturbations of the given one. A single inequality as well as semi-infinite constraint systems are considered.

Keywords: error bounds, Hoffman constants, subdifferential

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Published in SIAM Journal on Optimization 20 (2010), no. 6, 3280-3296. The original publication is available at http://link.aip.org/link/?SJE/20/3280

Download: [PDF]

Entry Submitted: 01/11/2010
Entry Accepted: 01/11/2010
Entry Last Modified: 12/03/2010

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