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A solution method for linear variational relation problems

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  • Anulekha Dhara
  • Dinh Luc

Abstract

In this paper, we consider a particular class of variational relation problem namely linear variational relation problem wherein the sets are defined by linear inequalities. The purpose is to study the existence of the solution set and its nature for this class of problem. Using these results, we provide algorithms to obtain the solutions of the problem based on which we present some numerical illustrations. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:59:y:2014:i:4:p:729-756
    DOI: 10.1007/s10898-013-0095-5
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. D. T. Luc, 2008. "An Abstract Problem in Variational Analysis," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 65-76, July.
    6. 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.
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