Journal of Convex Analysis 15 (2008), No. 1, 149--164
Copyright Heldermann Verlag 2008
Sequential Optimality Conditions in Convex Programming via Perturbation Approach
Radu Ioan Bot
Faculty of Mathematics, University of Technology, 09107 Chemnitz, Germany
radu.bot@mathematik.tu-chemnitz.de
Ernö Robert Csetnek
Faculty of Mathematics, University of Technology, 09107 Chemnitz, Germany
robert.csetnek@mathematik.tu-chemnitz.de
Gert Wanka
Faculty of Mathematics, University of Technology, 09107 Chemnitz, Germany
gert.wanka@mathematik.tu-chemnitz.de
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 Bröndsted-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, epsilon-subdifferential, sequential optimality conditions.
MSC: 90C25, 90C46, 47A55, 42A50
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