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Continuous convex sets and zero duality gap for convex programs

Emil ERNST(emil.ernst***at***univ-cezanne.fr)
Michel VOLLE(michel.volle***at***univ-avignon.fr)

Abstract: This article uses classical notions of convex analysis over euclidean spaces, like Gale & Klee’s boundary rays and asymptotes of a convex set, or the inner aperture directions defined by Larman and Brřndsted for the same class of sets, to provide a new zero duality gap criterion for ordinary convex programs. On this ground, we are able to characterize objective functions and respectively feasible sets for which the duality gap is always zero, re- gardless of the value of the constraints and respectively of the objective function.

Keywords: constrainedoptimization,recessionanalysis,convexprograms, continuous convex sets, inner aperture directions.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: unpublished: Aix-Marseille Universités, december 2011

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Entry Submitted: 12/15/2011
Entry Accepted: 12/16/2011
Entry Last Modified: 12/15/2011

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