Journal of Convex Analysis 31 (2024), No. 4, 1289--1304
Copyright Heldermann Verlag 2024
General Formulation of the S-Procedure
Michel Volle
Laboratoire de Mathématiques, Université d'Avignon, Avignon, France
michel.volle@univ-avignon.fr
Moussa Barro
Laboratoire de Mathématiques et d'Informatique, Université Nazi Boni, Bobo-Dioulasso, Burkina Faso
moussa.barro@alumni.univ-avignon.fr
We extend the S-procedure formulation to the general perturbational duality frame and give necessary and sufficient conditions for its validity, pointing out the hidden part of convexity.
Keywords: S-lemma, Farkas type Lemma, perturbational duality, separation of sets, Hahn-Banach Theorem, conjugacy.
MSC: 90C30, 90C46.
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