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Subdifferentials of nonconvex supremum functions and their applications to semi-infinite and infinite programs with Lipschitzian data

Boris Mordukhovich (boris***at***math.wayne.edu)
Nghia Tran (nghia***at***math.wayne.edu)

Abstract: The paper is devoted to the subdifferential study and applications of the supremum of uniformly Lipschitzian functions over arbitrary index sets with no topology. Based on advanced techniques of variational analysis, we evaluate major subdifferentials of the supremum functions in the general framework of Asplund (in particular, reflexive) spaces with no convexity or relaxation assumptions. The results obtained are applied to deriving new necessary optimality conditions for nonsmooth and nonconvex problems of semi-infinite and infinite programming

Keywords: Supremum function, Variational analysis, Generalized differentiation, Semi-infinite and infinite programming

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

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

Citation:

Download: [PDF]

Entry Submitted: 12/02/2011
Entry Accepted: 12/02/2011
Entry Last Modified: 11/30/2013

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