A note on partial calmness for bilevel optimization problems with linear structures at the lower level

Patrick Mehlitz, Leonid I. Minchenko, Alain B. Zemkoho

Published 2020-03-13Version 1

Partial calmness is a celebrated but restrictive property of bilevel optimization problems whose presence opens a way to the derivation of KKT-type necessary optimality conditions in order to characterize local minimizers. In the past, suffcient conditions for the validity of partial calmness have been investigated. In this regard, the presence of linear structures at the lower level problem has turned out to be beneffcial. However, the associated literature suffers from inaccurate results. In this note, we clarify some regarding erroneous statements and visualize the underlying issues with the aid of illustrative counterexamples.