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Tykhonov Well-Posedness for Quasi-Equilibrium Problems

Author

Listed:
  • M. Darabi

    (University of Isfahan)

  • J. Zafarani

    (Sheikhbahaee University and University of Isfahan)

Abstract

We consider an extension of the notion of Tykhonov well-posedness for perturbed vector quasi-equilibrium problems. We establish some necessary and sufficient conditions for verifying these well-posedness properties. As for applications of our results, the Tykhonov well-posedness of vector variational-like inequalities and vector optimization problems is established.

Suggested Citation

  • M. Darabi & J. Zafarani, 2015. "Tykhonov Well-Posedness for Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 458-479, May.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:2:d:10.1007_s10957-014-0630-7
    DOI: 10.1007/s10957-014-0630-7
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    1. Fang, Ya-Ping & Huang, Nan-Jing & Yao, Jen-Chih, 2010. "Well-posedness by perturbations of mixed variational inequalities in Banach spaces," European Journal of Operational Research, Elsevier, vol. 201(3), pages 682-692, March.
    2. L. Q. Anh & P. Q. Khanh, 2007. "On the Stability of the Solution Sets of General Multivalued Vector Quasiequilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 271-284, November.
    3. G. P. Crespi & A. Guerraggio & M. Rocca, 2007. "Well Posedness in Vector Optimization Problems and Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 213-226, January.
    4. L. C. Ceng & N. Hadjisavvas & S. Schaible & J. C. Yao, 2008. "Well-Posedness for Mixed Quasivariational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 109-125, October.
    5. L. Q. Anh & P. Q. Khanh & D. T. M. Van, 2012. "Well-Posedness Under Relaxed Semicontinuity for Bilevel Equilibrium and Optimization Problems with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 42-59, April.
    6. M. Balaj & L. J. Lin, 2013. "Existence Criteria for the Solutions of Two Types of Variational Relation Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 232-246, February.
    7. Gábor Kassay, 2010. "On Equilibrium Problems," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & Ider Tseveendorj (ed.), Optimization and Optimal Control, pages 55-83, Springer.
    8. G. P. Crespi & I. Ginchev & M. Rocca, 2004. "Minty Variational Inequalities, Increase-Along-Rays Property and Optimization1," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 479-496, December.
    9. M. Oveisiha & J. Zafarani, 2012. "Vector optimization problem and generalized convexity," Journal of Global Optimization, Springer, vol. 52(1), pages 29-43, January.
    10. Junyi Fu & Sanhua Wang, 2013. "Generalized strong vector quasi-equilibrium problem with domination structure," Journal of Global Optimization, Springer, vol. 55(4), pages 839-847, April.
    11. M. Bianchi & R. Pini, 2005. "Coercivity Conditions for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 79-92, January.
    12. Jacqueline Morgan, 2005. "Approximations and Well-Posedness in Multicriteria Games," Annals of Operations Research, Springer, vol. 137(1), pages 257-268, July.
    13. S. Al-Homidan & Q. H. Ansari, 2010. "Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 1-11, January.
    14. G. Wang & X. X. Huang, 2012. "Levitin–Polyak Well-Posedness for Optimization Problems with Generalized Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 27-41, April.
    15. San-hua Wang & Nan-jing Huang & Donal O’Regan, 2013. "Well-posedness for generalized quasi-variational inclusion problems and for optimization problems with constraints," Journal of Global Optimization, Springer, vol. 55(1), pages 189-208, January.
    16. R. P. Agarwal & M. Balaj & D. O’Regan, 2012. "A Unifying Approach to Variational Relation Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 417-429, November.
    17. J. W. Peng & S. Y. Wu, 2011. "The Well-Posedness for Multiobjective Generalized Games," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 416-423, August.
    18. T. Zolezzi, 2001. "Well-Posedness and Optimization under Perturbations," Annals of Operations Research, Springer, vol. 101(1), pages 351-361, January.
    19. G. P. Crespi & M. Papalia & M. Rocca, 2009. "Extended Well-Posedness of Quasiconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 285-297, May.
    20. M. Bianchi & G. Kassay & R. Pini, 2009. "Well-posedness for vector equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 171-182, August.
    21. Laura J. Kettner & Sien Deng, 2012. "On Well-Posedness and Hausdorff Convergence of Solution Sets of Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 619-632, June.
    22. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
    23. E. Miglierina & E. Molho, 2003. "Well-posedness and convexity in vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(3), pages 375-385, December.
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    1. L. Q. Anh & T. Q. Duy & D. V. Hien, 2020. "Well-posedness for the optimistic counterpart of uncertain vector optimization problems," Annals of Operations Research, Springer, vol. 295(2), pages 517-533, December.

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