Duality for convex infinite optimization on linear spaces

M. Goberna , M. Volle (1)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon

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.

Domaines: Optimisation et contrôle [math.OC]

M. Goberna, M. Volle. Duality for convex infinite optimization on linear spaces. Optimization Letters, 2022, ⟨10.1007/s11590-022-01865-x⟩. ⟨hal-03608012⟩