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

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

Author(s):
Bot, Radu Ioan
Grad, Sorin Mihai
Wanka, Gert
Title:
New regularity conditions for Lagrange and Fenchel-Lagrange duality in infinite dimensional spaces
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 13, 2006
Mathematics Subject Classification:
90C25 [ Convex programming ]
42A50 [ Conjugate functions, conjugate series, singular integrals ]
49N15 [ Duality theory ]
Abstract:
We give new regularity conditions based on epigraphs that assure strong duality between a given primal convex optimization problem and its Lagrange and Fenchel-Lagrange dual problems, respectively, in infinite dimensional spaces. Moreover we completely characterize through equivalent statements the so-called stable strong duality between the initial problem and the mentioned duals.
Keywords:
conjugate functions, Lagrange dual, Fenchel-Lagrange dual, constraint qualifications, epigraphs
Language:
English
Publication time:
7 / 2006