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Bot, Radu Ioan; Grad, Sorin Mihai; Wanka, Gert : A new constraint qualification and conjugate duality for composed convex optimization problems

Bot, Radu Ioan ; Grad, Sorin Mihai ; Wanka, Gert : A new constraint qualification and conjugate duality for composed convex optimization problems

Author(s):
Bot, Radu Ioan
Grad, Sorin Mihai
Wanka, Gert
Title:
A new constraint qualification and conjugate duality for composed convex optimization problems
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 15, 2004
Mathematics Subject Classification:
49N15 [ Duality theory ]
42A50 [ Conjugate functions, conjugate series, singular integrals ]
90C46 [ Optimality conditions, duality ]
Abstract:
We give a new constraint qualification which guarantees strong duality between a cone constrained convex optimization problem and its Fenchel-Lagrange dual. This result is applied to a convex optimization problem having, for a given non-empty closed convex cone K, as objective function a K-convex function postcomposed with a K-increasing convex function. For this so-called composed convex optimization problem we present a strong duality assertion, too, under weaker conditions than the ones considered so far. As application we show that the formula of the conjugate of a postcomposition with a K-increasing convex function is valid under weaker conditions than the ones existing in the literature.
Keywords:
Conjugate functions, Fenchel-Lagrange duality, composed convex optimization problems, cone constraint qualifications
Language:
English
Publication time:
10 / 2004