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

Electronic source:

application/pdf

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