Duality for convex infinite optimization on linear spaces

DOI10.1007/S11590-022-01865-XzbMATH Open1509.90146arXiv2106.14573MaRDI QIDQ6371401

Publication date: 28 June 2021

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.

Mathematics Subject Classification ID

Convex programming (90C25) Optimality conditions and duality in mathematical programming (90C46)

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