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