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On regular coderivatives in parametric equilibria with non-unique multipliers

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Abstract

This paper deals with the computation of regular coderivatives of solution maps associated with a frequently arising class of generalized equations (GEs). The constraint sets are given by (not necessarily convex) inequalities, and we do not assume linear independence of gradients to active constraints. The achieved results enable us to state several versions of sharp necessary optimality conditions in optimization problems with equilibria governed by such GEs. The advantages are illustrated by means of examples.

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Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117, Berlin, Germany

    R. Henrion

  2. Institute of Information Theory and Automation, Pod vodárenskou vezí 4, 18208, Praha 8, Czech Republic

    J. V. Outrata

  3. Centre for Informatics and Applied Optimization, University of Ballarat, P.O. Box 663, Ballarat, VIC, 3353, Australia

    J. V. Outrata

  4. Humboldt University Berlin, Unter den Linden 6, 10099, Berlin, Germany

    T. Surowiec

Authors
  1. R. Henrion
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  2. J. V. Outrata
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  3. T. Surowiec
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Corresponding author

Correspondence to J. V. Outrata.

Additional information

This work was supported by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin, by the Grant Agency of the Czech Academy of Sciences (Grant No. IAA 100750802) and by the Australian Research Council (Project DP 110102011).

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Henrion, R., Outrata, J.V. & Surowiec, T. On regular coderivatives in parametric equilibria with non-unique multipliers. Math. Program. 136, 111–131 (2012). https://doi.org/10.1007/s10107-012-0553-8

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  • DOI: https://doi.org/10.1007/s10107-012-0553-8

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