DC approach to regularity of convex multifunctions with applications to infinite systems

Boris Mordukhovich(borismath.wayne.edu)
Nghia Tran(nghiamath.wayne.edu)

Abstract: The paper develops a new approach to the study of metric regularity and related well-posedness properties of convex set-valued mappings between general Banach spaces by reducing them to unconstrained minimization problems with objectives given as the difference of convex (DC) functions. In this way we establish new formulas for calculating the exact regularity bound of closed and convex multifunctions and apply them to deriving explicit conditions ensuring well-posedness of infinite convex systems described by inequality and equality constraints.

Keywords: variational analysis, optimization, convex multifunctions, metric regularity

Category 1: Convex and Nonsmooth Optimization

Category 2: Infinite Dimensional Optimization (Semi-infinite Programming )

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Entry Submitted: 12/12/2011
Entry Accepted: 12/12/2011
Entry Last Modified: 12/12/2011

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