Abstract
In this paper, several Lagrange multiplier characterizations of the solution set of a convex infinite programming problem are given. Characterizations of solution sets of cone-constrained convex programs are derived as well. The procedure is then adopted to a semi-convex problem with convex constraints. For this problem, we present firstly a necessary and sufficient condition for optimality and secondly a characterization of its optimal solution set, based on a Lagrange multiplier associated with a given solution and on directional derivatives of the objective function.
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Son, T.Q., Dinh, N. Characterizations of optimal solution sets of convex infinite programs. TOP 16, 147–163 (2008). https://doi.org/10.1007/s11750-008-0039-2
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DOI: https://doi.org/10.1007/s11750-008-0039-2