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An Abstract Problem in Variational Analysis

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  • D. T. Luc

    (University of Avignon)

Abstract

The purpose of this paper is to present a unifying approach to study various models of equilibrium theory and variational inclusions. A simple condition is established for the existence of solutions of variational relations and is applied to a number of variational problems.

Suggested Citation

  • D. T. Luc, 2008. "An Abstract Problem in Variational Analysis," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 65-76, July.
    • Handle: RePEc:spr:joptap:v:138:y:2008:i:1:d:10.1007_s10957-008-9371-9
    DOI: 10.1007/s10957-008-9371-9
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    References listed on IDEAS

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    1. I. V. Konnov, 1998. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 165-181, October.
    2. Angelo Guerraggio & Nguyen Xuan Tan, 2002. "On general vector quasi-optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(3), pages 347-358, June.
    3. Angelo Guerraggio & Nguyen Xuan Tan, 2002. "On general vector quasi-optimization problems," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 347-358, June.
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    Cited by:

    1. Raúl Fierro, 2021. "An Intersection Theorem for Topological Vector Spaces and Applications," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 118-133, October.
    2. Ali Farajzadeh & Byung Soo Lee & Somyot Plubteing, 2016. "On Generalized Quasi-Vector Equilibrium Problems via Scalarization Method," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 584-599, February.
    3. Truong Duong & Nguyen Tan, 2012. "On the existence of solutions to generalized quasi-equilibrium problems," Journal of Global Optimization, Springer, vol. 52(4), pages 711-728, April.
    4. Phan Khanh & Lai Lin & Vo Long, 2014. "On topological existence theorems and applications to optimization-related problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(3), pages 253-272, June.
    5. Truong Duong, 2013. "Mixed generalized quasi-equilibrium problems," Journal of Global Optimization, Springer, vol. 56(2), pages 647-667, June.
    6. A. P. Farajzadeh & A. Amini-Harandi & K. R. Kazmi, 2010. "Existence of Solutions to Generalized Vector Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 95-104, July.
    7. M. Balaj & L. J. Lin, 2011. "Generalized Variational Relation Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 1-13, January.
    8. Anulekha Dhara & Dinh Luc, 2014. "A solution method for linear variational relation problems," Journal of Global Optimization, Springer, vol. 59(4), pages 729-756, August.
    9. 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.
    10. Pham Sach & Nguyen Minh, 2013. "Continuity of solution mappings in some parametric non-weak vector Ky Fan inequalities," Journal of Global Optimization, Springer, vol. 57(4), pages 1401-1418, December.
    11. 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.
    12. P. H. Sach & L. J. Lin & L. A. Tuan, 2010. "Generalized Vector Quasivariational Inclusion Problems with Moving Cones," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 607-620, December.
    13. P. Q. Khanh & V. S. T. Long & N. H. Quan, 2011. "Continuous Selections, Collectively Fixed Points and Weak Knaster–Kuratowski–Mazurkiewicz Mappings in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 552-572, December.
    14. Lai-Jiu Lin, 2012. "Variational relation problems and equivalent forms of generalized Fan-Browder fixed point theorem with applications to Stampacchia equilibrium problems," Journal of Global Optimization, Springer, vol. 53(2), pages 215-229, June.
    15. Zhe Yang & Yong Jian Pu, 2012. "Generalized Knaster–Kuratowski–Mazurkiewicz Theorem Without Convex Hull," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 17-29, July.
    16. Mircea Balaj, 2021. "Intersection theorems for generalized weak KKM set‐valued mappings with applications in optimization," Mathematische Nachrichten, Wiley Blackwell, vol. 294(7), pages 1262-1276, July.
    17. Phan Khanh & Vo Long, 2014. "Invariant-point theorems and existence of solutions to optimization-related problems," Journal of Global Optimization, Springer, vol. 58(3), pages 545-564, March.

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