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
- Electronic source:
-
application/pdf
- 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
