Journal of Convex Analysis 13 (2006), No. 3, 773--784
Copyright Heldermann Verlag 2006
A Qualification Free Sequential Pshenichnyi-Rockafellar Lemma and Convex Semidefinite Programming
Vaithilingam Jeyakumar
School of Mathematics, University of New South Wales, Sydney 2052, Australia
jeya@maths.unsw.edu.au
Zhi You Wu
School of Mathematics, University of New South Wales, Sydney 2052, Australia
Permanent Address: Dept. of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, P. R. China
zhiyouwu@maths.unsw.edu.au
Pshenichnyi-Rockafellar Lemma provides a necessary and sufficient condition for a minimizer of a lower semi-continuous convex function over a convex set whenever a qualification condition holds. In this paper we present sequential generalizations of the lemma without any qualification condition. As an application we derive qualification free optimality conditions for a more general convex semidefinite programming model problem.
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