Zero Duality Gap for Convex Programs: A Generalization of the Clark–Duffin Theorem

Emil Ernst () and Michel Volle ()
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Emil Ernst: Aix-Marseille Université, UMR7353
Michel Volle: Université d’Avignon et des Pays de Vaucluse

Journal of Optimization Theory and Applications, 2013, vol. 158, issue 3, No 3, 668-686

Abstract: 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 Brøndsted for the same class of sets, to provide a generalization of the Clark–Duffin Theorem. On this ground, we are able to characterize objective functions and, respectively, feasible sets for which the duality gap is always zero, regardless of the value of the constraints and, respectively, of the objective function.

Keywords: Constrained optimization; Zero duality gap; Continuous convex sets; Inner aperture directions (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-013-0287-7

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