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Relaxed Lagrangian duality in convex infinite optimization: reverse strong duality and optimality (2106.09299v1)
Published 17 Jun 2021 in math.OC
Abstract: We associate with each convex optimization problem posed on some locally convex space with an infinite index set T, and a given non-empty family H formed by finite subsets of T, a suitable Lagrangian-Haar dual problem. We provide reverse H-strong duality theorems, H-Farkas type lemmas and optimality theorems. Special attention is addressed to infinite and semi-infinite linear optimization problems.