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

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Abstract

Partial calmness is a celebrated but restrictive property of bilevel optimization problems whose presence opens a way to the derivation of Karush–Kuhn–Tucker-type necessary optimality conditions in order to characterize local minimizers. In the past, sufficient conditions for the validity of partial calmness have been investigated. In this regard, the presence of a linearly structured lower level problem has turned out to be beneficial. 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.

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Authors and Affiliations

  1. Brandenburgische Technische Universität Cottbus–Senftenberg, 03046, Cottbus, Germany

    Patrick Mehlitz

  2. Belarus State University of Informatics and Radioelectronics, 6 P. Brovki Street, Minsk, 220013, Belarus

    Leonid I. Minchenko

  3. School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK

    Alain B. Zemkoho

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  1. Patrick Mehlitz
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  2. Leonid I. Minchenko
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  3. Alain B. Zemkoho
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Correspondence to Patrick Mehlitz.

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Mehlitz, P., Minchenko, L.I. & Zemkoho, A.B. A note on partial calmness for bilevel optimization problems with linearly structured lower level. Optim Lett 15, 1277–1291 (2021). https://doi.org/10.1007/s11590-020-01636-6

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