Bot, Radu Ioan ; Csetnek, Ernö Robert ; Wanka, Gert : Sequential optimality conditions for composed convex optimization problems

Author(s):

Bot, Radu Ioan
Csetnek, Ernö Robert
Wanka, Gert

Title:

Sequential optimality conditions for composed convex optimization problems

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 12, 2007

Mathematics Subject Classification:

90C25			[ Convex programming ]
42A50			[ Conjugate functions, conjugate series, singular integrals ]
47A55			[ Perturbation theory ]
90C46			[ Optimality conditions, duality ]

Abstract:

Using a general approach which provides sequential optimality conditions for a general convex optimization problem, we derive necessary and sufficient optimality conditions for composed convex optimization problems. Further, we give sequential characterizations for a subgradient of the precomposition of a K-increasing lower semicontinuous convex function with a K-convex and K-epi-closed (continuous) function, where K is a nonempty convex cone. We prove that several results from the literature dealing with sequential characterizations of subgradients are obtained as particular cases of our results. We also improve the above mentioned statements.

Keywords:

convex programming, conjugate function, perturbation theory, sequential optimality conditions

Language:

English

Publication time:

6 / 2007