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

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1129-1135
Number of pages	7
Journal	Optimization Letters
Volume	16
Issue number	4
DOIs	https://doi.org/10.1007/s11590-021-01789-y
Publication status	Published - 1 May 2022

Keywords

Convexity of image sets
S-lemma
Separation of convex sets
Theorem of alternatives

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10.1007/s11590-021-01789-y

Cite this

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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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AB - 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.

KW - Convexity of image sets

KW - S-lemma

KW - Separation of convex sets

KW - Theorem of alternatives

UR - https://www.scopus.com/pages/publications/85111640539

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JO - Optimization Letters

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ER -

A fresh geometrical look at the general S-procedure

Abstract

Keywords

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