Relaxed Lagrangian duality in convex infinite optimization: reducibility and strong duality. (2nd January 2023) - Dinh, N.; Goberna, M. A.; López-Cerdá, M. A.; Volle, M.
Abstract : We associate with each convex optimization problem, posed on some locally convex space, with infinitely many constraints indexed by the set T, and a given non-empty family H of finite subsets of T, a suitable Lagrangian-Haar dual problem. We obtain necessary and sufficient conditions for H -reducibility, that is, equivalence to some subproblem obtained by replacing the whole index set T by some element of H . Special attention is addressed to linear optimization, infinite and semi-infinite, and to convex problems with a countable family of constraints. Results on zero H -duality gap and on H -(stable) strong duality are provided. Examples are given along the paper to illustrate the meaning of the results.