Geodesic
A Qualification Free Sequential Pshenichnyi-Rockafellar Lemma and Convex Semidefinite Programming
Journal of convex analysis, Tome 13 (2006) no. 3, pp. 773-784.

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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. 
@article{JCA_2006_13_3_JCA_2006_13_3_a18,
     author = {V. Jeyakumar and Z. Y. Wu},
     title = {A {Qualification} {Free} {Sequential} {Pshenichnyi-Rockafellar} {Lemma} and {Convex} {Semidefinite} {Programming}},
     journal = {Journal of convex analysis},
     pages = {773--784},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2006},
     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a18/}
}
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V. Jeyakumar; Z. Y. Wu. A Qualification Free Sequential Pshenichnyi-Rockafellar Lemma and Convex Semidefinite Programming. Journal of convex analysis, Tome 13 (2006) no. 3, pp. 773-784. http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a18/