Duality for convex infinite optimization on linear spaces

Miguel A. Goberna; Michel Volle

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arXiv · 2106.14573

Duality for convex infinite optimization on linear spaces

Miguel A. Goberna·Michel Volle

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Abstract

This note establishes a limiting formula for the conic Lagrangian dual of a convex infinite optimization problem, correcting the classical version of Karney [Math. Programming 27 (1983) 75-82] for convex semi-infinite programs. A reformulation of the convex infinite optimization problem with a single constraint leads to a limiting formula for the corresponding Lagrangian dual, called sup-dual, and also for the primal problem in the case when strong Slater condition holds, which also entails strong sup-duality.

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Miguel A. Goberna, Michel Volle. 2021-06-28. Duality for convex infinite optimization on linear spaces. https://arxiv.org/abs/2106.14573

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