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Vector Variational Inequality and Vector Pseudolinear Optimization

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  • X. Q. Yang

    (University of Western Australia)

Abstract

The study of a vector variational inequality has been advanced because it has many applications in vector optimization problems and vector equilibrium flows. In this paper, we discuss relations between a solution of a vector variational inequality and a Pareto solution or a properly efficient solution of a vector optimization problem. We show that a vector variational inequality is a necessary and sufficient optimality condition for an efficient solution of the vector pseudolinear optimization problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:3:d:10.1023_a:1022694427027
    DOI: 10.1023/A:1022694427027
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    References listed on IDEAS

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    1. 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.
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    Citations

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    Cited by:

    1. M. Golestani & H. Sadeghi & Y. Tavan, 2018. "Nonsmooth Multiobjective Problems and Generalized Vector Variational Inequalities Using Quasi-Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 896-916, December.
    2. Lu-Chuan Ceng & Shuechin Huang, 2010. "Existence theorems for generalized vector variational inequalities with a variable ordering relation," Journal of Global Optimization, Springer, vol. 46(4), pages 521-535, April.
    3. Ruiz-Garzon, G. & Osuna-Gomez, R. & Rufian-Lizana, A., 2004. "Relationships between vector variational-like inequality and optimization problems," European Journal of Operational Research, Elsevier, vol. 157(1), pages 113-119, August.
    4. S. K. Mishra & B. B. Upadhyay & Le Thi Hoai An, 2014. "Lagrange Multiplier Characterizations of Solution Sets of Constrained Nonsmooth Pseudolinear Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 763-777, March.
    5. 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.
    6. 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.
    7. S. Al-Homidan & Q. H. Ansari, 2010. "Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 1-11, January.

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