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Graphical Derivatives and Stability Analysis for Parameterized Equilibria with Conic Constraints

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Abstract

The paper concerns parameterized equilibria governed by generalized equations whose multivalued parts are modeled via regular normals to nonconvex conic constraints. Our main goal is to derive a precise pointwise second-order formula for calculating the graphical derivative of the solution maps to such generalized equations that involves Lagrange multipliers of the corresponding KKT systems and critical cone directions. Then we apply the obtained formula to characterizing a Lipschitzian stability notion for the solution maps that is known as isolated calmness.

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Authors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, MI, USA

    Boris S. Mordukhovich

  2. Institute of Information Theory and Automation, Czech Academy of Science, Prague, Czech Republic

    Jiri V. Outrata

  3. Centre for Informatics and Applied Optimization, Federation University of Australia, Ballarat, Australia

    Jiri V. Outrata

  4. Mathematical Engineering Department, Universidad de Chile, Santiago, Chile

    Héctor Ramírez C.

  5. Center for Mathematical Modeling, Universidad de Chile - CNRS, Santiago, Chile

    Héctor Ramírez C.

Authors
  1. Boris S. Mordukhovich
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  2. Jiri V. Outrata
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  3. Héctor Ramírez C.
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Corresponding author

Correspondence to Héctor Ramírez C..

Additional information

Dedicated to Lionel Thibault in honor of his 65th birthday.

Research of B. S. Mordukhovich was partly supported by the National Science Foundation under grant DMS-1007132.

Research of J. V. Outrata was partly supported by grant P201/12/0671 of the Grant Agency of the Czech Republic and the Australian Research Council under grant DP-110102011.

Research of H. Ramírez C. was partly supported by FONDECYT Project 1110888 and BASAL Project Centro de Modelamiento Matemático, Universidad de Chile.

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Mordukhovich, B.S., Outrata, J.V. & Ramírez C., H. Graphical Derivatives and Stability Analysis for Parameterized Equilibria with Conic Constraints. Set-Valued Var. Anal 23, 687–704 (2015). https://doi.org/10.1007/s11228-015-0328-5

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  • DOI: https://doi.org/10.1007/s11228-015-0328-5

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