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Descent and Penalization Techniques for Equilibrium Problems with Nonlinear Constraints

Author

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  • Giancarlo Bigi

    (Università di Pisa)

  • Mauro Passacantando

    (Università di Pisa)

Abstract

This paper deals with equilibrium problems with nonlinear constraints. Exploiting a gap function which relies on a polyhedral approximation of the feasible region, we propose two descent methods. They are both based on the minimization of a suitable exact penalty function, but they use different rules for updating the penalization parameter and they rely on different types of line search. The convergence of both algorithms is proved under standard assumptions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:3:d:10.1007_s10957-013-0473-7
    DOI: 10.1007/s10957-013-0473-7
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    6. 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.
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    9. 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.
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    Cited by:

    1. Giancarlo Bigi & Mauro Passacantando, 2016. "Gap functions for quasi-equilibria," Journal of Global Optimization, Springer, vol. 66(4), pages 791-810, December.
    2. Annel Thembinkosi Bokodisa & Lateef Olakunle Jolaoso & Maggie Aphane, 2021. "Halpern-Subgradient Extragradient Method for Solving Equilibrium and Common Fixed Point Problems in Reflexive Banach Spaces," Mathematics, MDPI, vol. 9(7), pages 1-24, March.
    3. 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.
    4. Dang Hieu & Pham Kim Quy, 2023. "One-Step iterative method for bilevel equilibrium problem in Hilbert space," Journal of Global Optimization, Springer, vol. 85(2), pages 487-510, February.
    5. Lateef Olakunle Jolaoso & Christian Chibueze Okeke & Yekini Shehu, 2021. "Extragradient Algorithm for Solving Pseudomonotone Equilibrium Problem with Bregman Distance in Reflexive Banach Spaces," Networks and Spatial Economics, Springer, vol. 21(4), pages 873-903, December.

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