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A fresh geometrical look at the general S-procedure

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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.

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Authors and Affiliations

  1. CERMICS, Ecole des Ponts, Marne-la-Vallée, France

    Michel De Lara

  2. Institut de Mathématiques, Université Paul Sabatier, Toulouse, France

    Jean-Baptiste Hiriart-Urruty

Authors
  1. Michel De Lara
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  2. Jean-Baptiste Hiriart-Urruty
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Correspondence to Michel De Lara.

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Lara, M.D., Hiriart-Urruty, JB. A fresh geometrical look at the general S-procedure. Optim Lett 16, 1129–1135 (2022). https://doi.org/10.1007/s11590-021-01789-y

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  • DOI: https://doi.org/10.1007/s11590-021-01789-y

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