A Fresh Geometrical Look at the General S-Procedure
Michel de Lara (ENPC, CERMICS), Jean-Baptiste Hiriart-Urruty (IMT)
TL;DR
This paper offers a new geometric perspective on the general S-procedure, establishing conditions based on convexity properties of data function images to determine its validity.
Contribution
It introduces a geometric framework for analyzing the S-procedure, providing necessary and nearly sufficient conditions based on convexity of augmented sets.
Findings
Identifies geometric conditions for S-procedure validity
Provides a necessary condition for the S-procedure to hold
Almost characterizes the S-procedure's applicability using convex hulls
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 (convex hulls, conical hulls) of images built from the data functions.
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