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On Calmness of the Argmin Mapping in Parametric Optimization Problems

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Abstract

Recently, Cánovas et al. presented an interesting result: the argmin mapping of a linear semi-infinite program under canonical perturbations is calm if and only if some associated linear semi-infinite inequality system is calm. Using classical tools from parametric optimization, we show that the if-direction of this condition holds in a much more general framework of optimization models, while the opposite direction may fail in the general case. In applications to special classes of problems, we apply a more recent result on the intersection of calm multifunctions.

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Acknowledgments

The authors would like to thank the two referees and the associate editor for their constructive comments.

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Authors and Affiliations

  1. IBW, Universität Zürich, Moussonstrasse 15, 8044, Zurich, Switzerland

    Diethard Klatte

  2. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Bernd Kummer

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  1. Diethard Klatte
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  2. Bernd Kummer
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Correspondence to Diethard Klatte.

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Communicated by Juan Parra.

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Klatte, D., Kummer, B. On Calmness of the Argmin Mapping in Parametric Optimization Problems. J Optim Theory Appl 165, 708–719 (2015). https://doi.org/10.1007/s10957-014-0643-2

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  • DOI: https://doi.org/10.1007/s10957-014-0643-2

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