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On Calmness of the Argmin Mapping in Parametric Optimization Problems

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  • Diethard Klatte

    (Universität Zürich)

  • Bernd Kummer

    (Humboldt-Universität zu Berlin)

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.

Suggested Citation

  • Diethard Klatte & Bernd Kummer, 2015. "On Calmness of the Argmin Mapping in Parametric Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 708-719, June.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:3:d:10.1007_s10957-014-0643-2
    DOI: 10.1007/s10957-014-0643-2
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    References listed on IDEAS

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    1. Stephen M. Robinson, 1976. "Regularity and Stability for Convex Multivalued Functions," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 130-143, May.
    2. M. J. Cánovas & A. Hantoute & J. Parra & F. J. Toledo, 2014. "Calmness of the Argmin Mapping in Linear Semi-Infinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 111-126, January.
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    Cited by:

    1. M. J. Cánovas & R. Henrion & M. A. López & J. Parra, 2016. "Outer Limit of Subdifferentials and Calmness Moduli in Linear and Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 925-952, June.

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