A fresh geometrical look at the general S-procedure

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.

Automated summary

The study revisits the S-procedure for general functions with geometrical glasses, outlining a necessary condition and almost a sufficient condition for the validity of the S-procedure, all expressed in terms of convexity of augmented sets built from the data functions.