A fresh geometrical look at the general S-procedure

Michel De Lara; Jean Baptiste Hiriart-Urruty

doi:10.1007/s11590-021-01789-y

A fresh geometrical look at the general S-procedure

Michel De Lara
, Jean Baptiste Hiriart-Urruty

Université de Toulouse

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

5 Citations (Scopus)

Résumé

We revisit the S-procedure for general functions with “geometrical glasses”. We thus delineate a necessary condition, and almost a sufficient condition, to have the S-procedure valid. Everything is expressed in terms of convexity of augmented sets (i.e., via convex hulls, conical hulls) of images built from the data functions.

langue originale	Anglais
Pages (de - à)	1129-1135
Nombre de pages	7
journal	Optimization Letters
Volume	16
Numéro de publication	4
Les DOIs	https://doi.org/10.1007/s11590-021-01789-y
état	Publié - 1 mai 2022

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10.1007/s11590-021-01789-y

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abstract = "We revisit the S-procedure for general functions with {\textquotedblleft}geometrical glasses{\textquotedblright}. We thus delineate a necessary condition, and almost a sufficient condition, to have the S-procedure valid. Everything is expressed in terms of convexity of augmented sets (i.e., via convex hulls, conical hulls) of images built from the data functions.",

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KW - S-lemma

KW - Separation of convex sets

KW - Theorem of alternatives

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A fresh geometrical look at the general S-procedure

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