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Bot, Radu Ioan; Grad, Sorin Mihai; Wanka, Gert : New regularity conditions for strong and total Lagrange duality

Bot, Radu Ioan ; Grad, Sorin Mihai ; Wanka, Gert : New regularity conditions for strong and total Lagrange duality

Author(s):
Bot, Radu Ioan
Grad, Sorin Mihai
Wanka, Gert
Title:
New regularity conditions for strong and total Lagrange duality
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 3, 2007
Mathematics Subject Classification:
49N15 [ Duality theory ]
90C25 [ Convex programming ]
90C34 [ Semi-infinite programming ]
Abstract:
We give some new regularity conditions for convex optimization problems in separated locally convex spaces which completely characterize the stable strong and strong Lagrange duality and, respectively, the stable strong and strong Lagrange duality for the case when a solution of the primal problem is assumed as known, situations named here total and, respectively, stable total duality. In particular instances the conditions we consider turn into some other constraint qualifications known in the literature, like dual CQ, Farkas-Minkowski CQ, locally Farkas-Minkowski CQ and basic CQ. We show that our new results extend some existing ones in the literature.
Keywords:
conjugate functions, Lagrange dual problem, basic constraint qualification, (locally) Farkas-Minkowski condition, stable strong duality
Language:
English
Publication time:
2 / 2007