Bot, Radu Ioan ; Csetnek, Ernö Robert ; Wanka, Gert : Sequential optimality conditions in convex programming via perturbation approach

Author(s):

Bot, Radu Ioan
Csetnek, Ernö Robert
Wanka, Gert

Title:

Sequential optimality conditions in convex programming via perturbation approach

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 23, 2006

Mathematics Subject Classification:

90C25			[ Convex programming ]
90C46			[ Optimality conditions, duality ]
47A55			[ Perturbation theory ]

Abstract:

In this paper a necessary and sufficient sequential optimality condition without a constraint qualification for a general convex optimization problem is given in terms of the ε - subdifferential. Further, a sequential characterization of optimal solutions involving the convex subdifferential is derived using a version of the Brøndsted-Rockafellar Theorem. We prove that some results from the literature concerning sequential generalizations of the Pshenichnyi-Rockafellar Lemma are obtained as particular cases of our results. Moreover, by this general approach we succeed to improve some sequential Lagrange multiplier conditions given in the past.

Keywords:

convex programming, conjugate function, ε - subdifferential, sequential optimality conditions

Language:

English

Publication time:

1 / 2007