A Qualification Free Sequential Pshenichnyi-Rockafellar Lemma and Convex Semidefinite Programming

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