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Bot, Radu Ioan; Grad, Sorin-Mihai; Wanka, Gert : New regularity conditions for strong and total Fenchel-Lagrange duality in infinite dimensional spaces

Bot, Radu Ioan ; Grad, Sorin-Mihai ; Wanka, Gert : New regularity conditions for strong and total Fenchel-Lagrange duality in infinite dimensional spaces

Author(s):
Bot, Radu Ioan
Grad, Sorin-Mihai
Wanka, Gert
Title:
New regularity conditions for strong and total Fenchel-Lagrange duality in infinite dimensional spaces
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 9, 2007
Mathematics Subject Classification:
49N15 [ Duality theory ]
90C25 [ Convex programming ]
90C34 [ Semi-infinite programming ]
Abstract:
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, respectively, stable total Fenchel-Lagrange duality. For particular settings the conditions 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 in the literature.
Keywords:
Conjugate functions, Fenchel-Lagrange dual, constraint qualifications, (locally) Farkas-Minkowski condition, stable strong duality
Language:
English
Publication time:
3 / 2007