Metric regularity and systems of generalized equations

Andrei V. Dmitruk (dmitrukmember.ams.org)
Alexander Y. Kruger (a.krugerballarat.edu.au)

Abstract: The paper is devoted to a revision of the metric regularity property for mappings between metric or Banach spaces. Some new concepts are introduced: uniform metric regularity, metric regularity along a subspace, strong metric regularity for mappings into product spaces, when each component is perturbed independently. Regularity criteria are established based on a nonlocal version of Lyusternik-Graves theorem due to Milyutin. The criteria are applied to systems of generalized equations producing some "error bound" type results

Keywords: Variational analysis, Lyusternik-Graves theorem, regularity, set-valued mapping, constraint qualification

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Published in J. Math. Anal. Appl. 342 (2008), no. 2, 864–873. The original publication is available at www.sciencedirect.com; doi:10.1016/j.jmaa.2007.12.057

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Entry Submitted: 10/08/2006
Entry Accepted: 10/08/2006
Entry Last Modified: 03/20/2008

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