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New regularity conditions for strong and total Fenchel-Lagrange duality in infinite dimensional spaces. (English) Zbl 1142.49015
Summary: We give new regularity conditions for convex optimization problems in separated locally convex spaces. We completely characterize the stable strong and strong Fenchel-Lagrange duality. Then we give similar statements for the case when a solution of the primal problem is assumed as known, obtaining complete characterizations for the so-called total and stable total Fenchel-Lagrange duality, respectively. For particular settings the conditions that we consider turn into some constraint qualifications already used by different authors, like Farkas-Minkowski $CQ$, locally Farkas-Minkowski $CQ$ and basic $CQ$, and we rediscover and improve some recent results from the literature.
##### MSC:
 49N15 Duality theory (optimization) 90C25 Convex programming 90C34 Semi-infinite programming 49N60 Regularity of solutions in calculus of variations