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Some Remarks on Stability of Generalized Equations

Author

Listed:
  • René Henrion

    (Weierstrass Institute for Applied Analysis and Stochastics)

  • Alexander Y. Kruger

    (University of Ballarat)

  • Jiří V. Outrata

    (Academy of Sciences of the Czech Republic)

Abstract

The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multivalued term amounts to the regular normal cone to a (possibly nonconvex) set given by C 2 inequalities. Instead of the linear independence qualification condition, standardly used in this context, one assumes a combination of the Mangasarian–Fromovitz and the constant rank qualification conditions. Based on the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constraints are derived, and a workable characterization of the isolated calmness of the considered solution map is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:3:d:10.1007_s10957-012-0147-x
    DOI: 10.1007/s10957-012-0147-x
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    Citations

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    Cited by:

    1. H. Gfrerer & J. V. Outrata, 2017. "On the Aubin property of a class of parameterized variational systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(3), pages 443-467, December.
    2. Roberto Andreani & Gabriel Haeser & Leonardo M. Mito & C. Héctor Ramírez & Thiago P. Silveira, 2022. "Global Convergence of Algorithms Under Constant Rank Conditions for Nonlinear Second-Order Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 42-78, October.
    3. Matthieu Maréchal, 2018. "Metric Subregularity in Generalized Equations," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 541-558, March.
    4. Helmut Gfrerer & Jiří V. Outrata, 2016. "On Computation of Generalized Derivatives of the Normal-Cone Mapping and Their Applications," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1535-1556, November.
    5. B. S. Mordukhovich & T. T. A. Nghia & R. T. Rockafellar, 2015. "Full Stability in Finite-Dimensional Optimization," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 226-252, February.

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