Abstract

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

Author information

Contact details are reproduced from the original publication and may be historical.

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

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Suggested citation

V. Jeyakumar, Z. Y. Wu. “A Qualification Free Sequential Pshenichnyi-Rockafellar Lemma and Convex Semidefinite Programming.” Journal of Convex Analysis 13 (2006), No. 3/4, 773–784. https://doi.org/10.68381/jca13058

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Published by Heldermann Verlag, 2006. Rights now held by Banach Press LLC.