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Strong Stationarity Conditions for a Class of Optimization Problems Governed by Variational Inequalities of the Second Kind

Author

Listed:
  • J. C. Reyes

    (EPN Quito)

  • C. Meyer

    (Technische Universität Dortmund)

Abstract

We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal–dual reformulation of the governing inequality, the differentiability of the solution map is studied. Directional differentiability is proved both for finite-dimensional problems and for problems in function spaces, under suitable assumptions on the active set. A characterization of Bouligand and strong stationary points is obtained thereafter. Finally, based on the obtained first-order information, a trust-region algorithm is proposed for the solution of the optimization problems.

Suggested Citation

  • J. C. Reyes & C. Meyer, 2016. "Strong Stationarity Conditions for a Class of Optimization Problems Governed by Variational Inequalities of the Second Kind," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 375-409, February.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:2:d:10.1007_s10957-015-0748-2
    DOI: 10.1007/s10957-015-0748-2
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    References listed on IDEAS

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    1. Karl Kunisch & Daniel Wachsmuth, 2012. "Path-following for optimal control of stationary variational inequalities," Computational Optimization and Applications, Springer, vol. 51(3), pages 1345-1373, April.
    2. Juan Reyes, 2012. "Optimization of mixed variational inequalities arising in flow of viscoplastic materials," Computational Optimization and Applications, Springer, vol. 52(3), pages 757-784, July.
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