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 of finite subsets of T, a suitable Lagrangian-Haar dual problem. We obtain necessary and sufficient conditions for -reducibility, that is, equivalence to some subproblem obtained by replacing the whole index set T by some element of . Special attention is addressed to linear optimization, infinite and semi-infinite, and to convex problems with a countable family of constraints. Results on zero -duality gap and on -(stable) strong duality are provided. Examples are given along the paper to illustrate the meaning of the results.
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