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

Electronic source:

application/pdf

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