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We associate with each convex optimization problem posed on some locallyconvex space with an infinite index set T, and a given non-empty family Hformed by finite subsets of T, a suitable Lagrangian-Haar dual problem. Weprovide reverse H-strong duality theorems, H-Farkas type lemmas and optimalitytheorems. Special attention is addressed to infinite and semi-infinite linearoptimization problems.

Relaxed Lagrangian duality in convex infinite optimization: reverse strong duality and optimality