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Metric Subregularity in Generalized Equations

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  • Matthieu Maréchal

    (Universidad Diego Portales)

Abstract

In this article, we study the metric subregularity of generalized equations using a new tool of nonsmooth analysis. We obtain a sufficient condition for a generalized equation to be metrically subregular, which is not a necessary condition for metric regularity, using a subtle adjustment of the Mordukhovich coderivative. We apply these results to the study of the metric subregularity in a Cournot duopoly game.

Suggested Citation

  • Matthieu Maréchal, 2018. "Metric Subregularity in Generalized Equations," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 541-558, March.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:3:d:10.1007_s10957-018-1246-0
    DOI: 10.1007/s10957-018-1246-0
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    References listed on IDEAS

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    1. S. Adly & R. Cibulka, 2014. "Quantitative Stability of a Generalized Equation," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 90-110, January.
    2. René Henrion & Alexander Y. Kruger & Jiří V. Outrata, 2013. "Some Remarks on Stability of Generalized Equations," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 681-697, December.
    3. T. Chuong & A. Kruger & J.-C. Yao, 2011. "Calmness of efficient solution maps in parametric vector optimization," Journal of Global Optimization, Springer, vol. 51(4), pages 677-688, December.
    4. Boris Mordukhovich & Wei Ouyang, 2015. "Higher-order metric subregularity and its applications," Journal of Global Optimization, Springer, vol. 63(4), pages 777-795, December.
    Full references (including those not matched with items on IDEAS)

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