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On Relations Between Vector Optimization Problems and Vector Variational Inequalities

Author

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  • D.E. Ward

    (Miami University)

  • G.M. Lee

    (Pukyong National University)

Abstract

We obtain equivalences between weak Pareto solutions of vector optimization problems and solutions of vector variational inequalities involving generalized directional derivatives.

Suggested Citation

  • D.E. Ward & G.M. Lee, 2002. "On Relations Between Vector Optimization Problems and Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 583-596, June.
    • Handle: RePEc:spr:joptap:v:113:y:2002:i:3:d:10.1023_a:1015364905959
    DOI: 10.1023/A:1015364905959
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    References listed on IDEAS

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    1. X. Q. Yang, 1997. "Vector Variational Inequality and Vector Pseudolinear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 729-734, December.
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    Cited by:

    1. S. Li & M. Li, 2009. "Levitin–Polyak well-posedness of vector equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 125-140, March.
    2. Do Luu, 2016. "Optimality Condition for Local Efficient Solutions of Vector Equilibrium Problems via Convexificators and Applications," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 643-665, November.
    3. M. Oveisiha & J. Zafarani, 2012. "Vector optimization problem and generalized convexity," Journal of Global Optimization, Springer, vol. 52(1), pages 29-43, January.
    4. Do Luu & Dinh Hang, 2014. "Efficient solutions and optimality conditions for vector equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 163-177, April.
    5. X. M. Yang & X. Q. Yang & K. L. Teo, 2004. "Some Remarks on the Minty Vector Variational Inequality," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 193-201, April.

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