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

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
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