A weak constraint qualification for conic programs and a problem on\n duality gap

2015/04/21 by Bruno F. Lourenço, Lourenço, Bruno F.
Computer Science · Engineering · Mathematics · #49N15 #90C46 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Vehicle Routing Optimization Methods

paper · pdf · doi:10.48550/arxiv.1504.05630

openalex publication_date 2015/04/21 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We discuss a weak constraint qualification for conic linear programs and its\napplications for a few classes of cones. This constraint qualification is used\nto give a solution to a problem proposed by Shapiro and Z valinescu and show\nthat if a closed convex cone is such that all its non-trivial faces are\npolyhedral and all the non-trivial exposed faces of its dual are polyhedral,\nthen the duality gap is zero as long as the primal and dual problems are\nfeasible. Moreover, the common optimal value must be attained at least at one\nof the sides. We also show an example of a cone that meets the requirements our\ntheorem but is such that previously known results cannot be used to prove its\ngood duality properties.\n

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