https://hal-univ-avignon.archives-ouvertes.fr/hal-03608012Goberna, M.M.GobernaVolle, M.M.VolleLMA - EA2151 Laboratoire de MathÃ©matiques d'Avignon - AU - Avignon UniversitÃ©Duality for convex infinite optimization on linear spacesHAL CCSD2022[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Volle, Michel2022-03-14 14:25:282022-03-15 03:13:062022-03-14 14:25:28enJournal articles10.1007/s11590-022-01865-x1Abstract 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.