https://hal-univ-avignon.archives-ouvertes.fr/hal-03540267Goberna, MMGobernaVolle, MMVolleLMA - EA2151 Laboratoire de Mathématiques d'Avignon - AU - Avignon UniversitéDuality for convex infinite optimization on linear spacesHAL CCSD2022[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Volle, Michel2022-01-23 16:46:342022-02-22 11:36:042022-02-01 16:19:53enPreprints, Working Papers, ...application/pdf1This 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-in…nite programs. A reformulation of the convex infinite optimization problem with a single constraint leads to a limiting formula for the corresponding Lagrangian dual, called supdual, and also for the primal problem in the case when strong Slater condition holds, which also entails strong sup-duality.