A note on partial calmness for bilevel optimization problems with\n linearly structured lower level

Partial calmness is a celebrated but restrictive property of bilevel\noptimization problems whose presence opens a way to the derivation of\nKarush--Kuhn--Tucker-type necessary optimality conditions in order to\ncharacterize local minimizers. In the past, sufficient conditions for the\nvalidity of partial calmness have been investigated. In this regard, the\npresence of a linearly structured lower level problem has turned out to be\nbeneficial. However, the associated literature suffers from inaccurate results.\nIn this note, we clarify some regarding erroneous statements and visualize the\nunderlying issues with the aid of illustrative counterexamples.\n