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Equilibrium Problems with Generalized Monotone Bifunctions and Applications to Variational Inequalities

Author

Listed:
  • O. Chaldi

    (University Cadi Ayyad)

  • Z. Chbani

    (University Cadi Ayyad)

  • H. Riahi

    (University Cadi Ayyad)

Abstract

This paper attempts to generalize and unify several new results that have been obtained in the ongoing research area of existence of solutions for equilibrium problems. First, we propose sufficient conditions, which include generalized monotonicity and weak coercivity conditions, for existence of equilibrium points. As consequences, we generalize various recent theorems on the existence of such solutions. For applications, we treat some generalized variational inequalities and complementarity problems. In addition, considering penalty functions, we study the position of a selected solution by relying on the viscosity principle.

Suggested Citation

  • O. Chaldi & Z. Chbani & H. Riahi, 2000. "Equilibrium Problems with Generalized Monotone Bifunctions and Applications to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 105(2), pages 299-323, May.
    • Handle: RePEc:spr:joptap:v:105:y:2000:i:2:d:10.1023_a:1004657817758
    DOI: 10.1023/A:1004657817758
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    References listed on IDEAS

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    1. Monica Bianchi, 1993. "Una classe di funzioni monotone generalizzate," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 16(1), pages 17-32, March.
    2. Romesh Saigal, 1976. "Extension of the Generalized Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 260-266, August.
    3. R. C. Riddell, 1981. "Equivalence of Nonlinear Complementarity Problems and Least Element Problems in Banach Lattices," Mathematics of Operations Research, INFORMS, vol. 6(3), pages 462-474, August.
    4. Richard W. Cottle & Jong-Shi Pang, 1978. "A Least-Element Theory of Solving Linear Complementarity Problems as Linear Programs," Mathematics of Operations Research, INFORMS, vol. 3(2), pages 155-170, May.
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    Citations

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    Cited by:

    1. O. Chadli & Z. Liu & J. C. Yao, 2007. "Applications of Equilibrium Problems to a Class of Noncoercive Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 89-110, January.
    2. Majdi Argoubi & Emna Ammari & Hatem Masri, 2021. "A scientometric analysis of Operations Research and Management Science research in Africa," Operational Research, Springer, vol. 21(3), pages 1827-1843, September.
    3. Y. Chiang & O. Chadli & J.C. Yao, 2003. "Existence of Solutions to Implicit Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 116(2), pages 251-264, February.
    4. Y. Chiang & O. Chadli & J. Yao, 2004. "Generalized Vector Equilibrium Problems with Trifunctions," Journal of Global Optimization, Springer, vol. 30(2), pages 135-154, November.
    5. Lam Quoc Anh & Tran Quoc Duy & Le Dung Muu & Truong Van Tri, 2021. "The Tikhonov regularization for vector equilibrium problems," Computational Optimization and Applications, Springer, vol. 78(3), pages 769-792, April.
    6. A. Lahmdani & O. Chadli & J. C. Yao, 2014. "Existence of Solutions for Noncoercive Hemivariational Inequalities by an Equilibrium Approach Under Pseudomonotone Perturbation," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 49-66, January.
    7. N. X. Hai & P. Q. Khanh, 2007. "Existence of Solutions to General Quasiequilibrium Problems and Applications," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 317-327, June.
    8. John Cotrina & Anton Svensson, 2021. "The finite intersection property for equilibrium problems," Journal of Global Optimization, Springer, vol. 79(4), pages 941-957, April.
    9. O. Chadli & S. Schaible & J. C. Yao, 2004. "Regularized Equilibrium Problems with Application to Noncoercive Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 571-596, June.
    10. L.J. Lin & Q.H. Ansari & J.Y. Wu, 2003. "Geometric Properties and Coincidence Theorems with Applications to Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 121-137, April.
    11. Ouayl Chadli & Qamrul Hasan Ansari & Suliman Al-Homidan, 2017. "Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 726-758, March.
    12. G. Bento & J. Cruz Neto & J. Lopes & A. Soares Jr & Antoine Soubeyran, 2016. "Generalized Proximal Distances for Bilevel Equilibrium Problems," Post-Print hal-01690192, HAL.
    13. O. Chadli & N.C. Wong & J.C. Yao, 2003. "Equilibrium Problems with Applications to Eigenvalue Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 245-266, May.
    14. M. Bianchi & I. Konnov & R. Pini, 2010. "Lexicographic and sequential equilibrium problems," Journal of Global Optimization, Springer, vol. 46(4), pages 551-560, April.
    15. M. Fakhar & J. Zafarani, 2004. "Generalized Equilibrium Problems for Quasimonotone and Pseudomonotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 349-364, November.
    16. Q. H. Ansari & I. V. Konnov & J. C. Yao, 2001. "Existence of a Solution and Variational Principles for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 481-492, September.
    17. Abdellatif Moudafi, 2010. "Proximal methods for a class of bilevel monotone equilibrium problems," Journal of Global Optimization, Springer, vol. 47(2), pages 287-292, June.
    18. 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.
    19. Phan Tu Vuong & Jean Jacques Strodiot, 2020. "A Dynamical System for Strongly Pseudo-monotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 767-784, June.

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