TY - JOUR
T1 - A fresh geometrical look at the general S-procedure
AU - Lara, Michel De
AU - Hiriart-Urruty, Jean Baptiste
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022/5/1
Y1 - 2022/5/1
N2 - 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.
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
U2 - 10.1007/s11590-021-01789-y
DO - 10.1007/s11590-021-01789-y
M3 - Article
AN - SCOPUS:85111640539
SN - 1862-4472
VL - 16
SP - 1129
EP - 1135
JO - Optimization Letters
JF - Optimization Letters
IS - 4
ER -