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On Lexicographic Vector Equilibrium Problems

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Abstract

We consider vector equilibrium problems using the lexicographic order. We show that several classes of inverse lexicographic optimization problems can be reduced to lexicographic vector equilibrium problems. Some approaches to solve such problems are also suggested.

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References

  1. Konnov, I.V., Combined Relaxation Method for Solving Vector Equilibrium Problems, Russian Mathematics (Iz. VUZ), Vol. 39, No. 12, pp. 51-59, 1995.

    Google Scholar 

  2. Hadjisavvas, N., and Schaible, S., From Scalar to Vector Equilibrium Problems in the Quasimonotone Case, Journal of Optimization Theory and Applications, Vol. 96, pp. 297-305, 1998.

    Google Scholar 

  3. Giannessi, F., Editor, Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Kluwer Academic Publishers, Dordrecht, Netherlands, 2000.

    Google Scholar 

  4. Fishburn, P.C., Lexicographic Order, Utilities, and Decision Rules: A Survey, Management Science, Vol. 20, pp. 1442-1471, 1974.

    Google Scholar 

  5. Podinovskii, V. V., and Gavrilov, V.M., Optimization with Respect to Sequentially Applied Criteria, Sovetskoe Radio, Moscow, USSR, 1976 (in Russian).

    Google Scholar 

  6. Martinez-Legaz, J. E., Lexicographical Order, Inequality Systems, and Optimization, Systems Modelling and Optimization, Edited by P. Thoft-Christensen, Springer Verlag, Berlin, Germany, pp. 203-212, 1984.

    Google Scholar 

  7. Konnov, I.V., On Vector Equilibrium and Vector Variational Inequality Problems, Generalized Convexity and Generalized Monotonicity, Edited by N. Hadjisavvas, J. E. Martinez-Legaz, and J. P. Penot, Springer Verlag, Berlin, Germany, pp. 247-263, 2001.

    Google Scholar 

  8. Martinez-Legaz, J.E., Lexicographical Order and Duality in Multiobjective Programming, European Journal of Operations Research, Vol. 33, pp. 342-348, 1988.

    Google Scholar 

  9. Yang, X. Q., and Goh, C. J., On Vector Variational Inequalities: Application to Vector Equilibria, Journal of Optimization Theory and Applications, Vol. 95, pp. 431-443, 1997.

    Google Scholar 

  10. Konnov, I.V., Dual Approach for a Class of Mixed Variational Inequalities, Computational Mathematics and Mathematical Physics (to appear).

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Authors and Affiliations

  1. Department of Applied Mathematics, Kazan University, Kazan, Russia

    I.V. Konnov (Professor)

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  1. I.V. Konnov
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Konnov, I. On Lexicographic Vector Equilibrium Problems. Journal of Optimization Theory and Applications 118, 681–688 (2003). https://doi.org/10.1023/B:JOTA.0000004877.39408.80

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  • DOI: https://doi.org/10.1023/B:JOTA.0000004877.39408.80

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