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On Lexicographic Vector Equilibrium Problems

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  • I.V. Konnov

    (Kazan University)

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.

Suggested Citation

  • I.V. Konnov, 2003. "On Lexicographic Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 681-688, September.
    • Handle: RePEc:spr:joptap:v:118:y:2003:i:3:d:10.1023_b:jota.0000004877.39408.80
    DOI: 10.1023/B:JOTA.0000004877.39408.80
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    References listed on IDEAS

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    1. Igor V. Konnov & Dinh The Luc & Alexander M. Rubinov, 2006. "Generalized Convexity and Related Topics," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-37007-9, July.
    2. I. V. Konnov, 2001. "Combined Relaxation Method for Monotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 327-340, November.
    3. Martinez-Legaz, Juan Enrique, 1988. "Lexicographical order and duality in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 33(3), pages 342-348, February.
    4. X. Q. Yang & C. J. Goh, 1997. "On Vector Variational Inequalities: Application to Vector Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 431-443, November.
    5. N. Hadjisavvas & S. Schaible, 1998. "From Scalar to Vector Equilibrium Problems in the Quasimonotone Case," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 297-309, February.
    6. Peter C. Fishburn, 1974. "Exceptional Paper--Lexicographic Orders, Utilities and Decision Rules: A Survey," Management Science, INFORMS, vol. 20(11), pages 1442-1471, July.
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    Cited by:

    1. I. Konnov, 2013. "Vector network equilibrium problems with elastic demands," Journal of Global Optimization, Springer, vol. 57(2), pages 521-531, October.
    2. M. Bianchi & I. Konnov & R. Pini, 2010. "Lexicographic and sequential equilibrium problems," Journal of Global Optimization, Springer, vol. 46(4), pages 551-560, April.

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