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
