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Optimization Tools for Solving Equilibrium Problems with Nonsmooth Data

Author

Listed:
  • Giancarlo Bigi

    (Università di Pisa)

  • Massimo Pappalardo

    (Università di Pisa)

  • Mauro Passacantando

    (Università di Pisa)

Abstract

The paper deals with the gap function approach for equilibrium problems with locally Lipschitz data. The gap function inherits the locally Lipschitz continuity of the data. Hence, the connections between its generalized directional derivatives, monotonicity conditions on the equilibrium bifunction and descent properties, can be analyzed. In turn, this analysis leads to devise two descent methods. Finally, the results of preliminary numerical tests are reported.

Suggested Citation

  • Giancarlo Bigi & Massimo Pappalardo & Mauro Passacantando, 2016. "Optimization Tools for Solving Equilibrium Problems with Nonsmooth Data," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 887-905, December.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:3:d:10.1007_s10957-016-0974-2
    DOI: 10.1007/s10957-016-0974-2
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    References listed on IDEAS

    as
    1. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    2. K. F. Ng & L. L. Tan, 2007. "D-Gap Functions for Nonsmooth Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 77-97, April.
    3. Jean Strodiot & Thi Nguyen & Van Nguyen, 2013. "A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems," Journal of Global Optimization, Springer, vol. 56(2), pages 373-397, June.
    4. Giancarlo Bigi & Mauro Passacantando, 2012. "Gap functions and penalization for solving equilibrium problems with nonlinear constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 323-346, October.
    5. Giancarlo Bigi & Mauro Passacantando, 2015. "Descent and Penalization Techniques for Equilibrium Problems with Nonlinear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 804-818, March.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Sajjad Kazemi & Nader Kanzi, 2018. "Constraint Qualifications and Stationary Conditions for Mathematical Programming with Non-differentiable Vanishing Constraints," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 800-819, December.
    2. Fan-Yun Meng & Li-Ping Pang & Jian Lv & Jin-He Wang, 2017. "An approximate bundle method for solving nonsmooth equilibrium problems," Journal of Global Optimization, Springer, vol. 68(3), pages 537-562, July.

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