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Error bounds: necessary and sufficient conditions

Marian J. Fabian (fabian***at***math.cas.cz)
Ren\'e Henrion (henrion***at***wias-berlin.de)
Alexander Y. Kruger (a.kruger***at***ballarat.edu.au)
Ji\v{r}\'i V. Outrata (outrata***at***utia.cas.cz)

Abstract: The paper presents a general classiffication scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space.

Keywords: Error bounds; Calmness; Subdifferential; Slope

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Published in Set-Valued and Variational Analysis 18 (2010), no. 2, 121149. The original publication is available electronically on SpringerLink: http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s11228-010-0133-0. August 5, 2010. Correction: Proposition 10 (iii) is valid in Asplund spaces.

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Entry Submitted: 02/25/2009
Entry Accepted: 02/25/2009
Entry Last Modified: 08/04/2010

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