A Result on Vector Variational Inequalities with Polyhedral Constraint Sets
- 93 Downloads
In this note, by using some well-known results on properly efficient solutions of vector optimization problems, we show that the Pareto solution set of a vector variational inequality with a polyhedral constraint set can be expressed as the union of the solution sets of a family of (scalar) variational inequalities.
Unable to display preview. Download preview PDF.
- 1.Giannessi, F., Theorems of Alternative, Quadratic Programs, and Complementarity Problems, Variational Inequalities and Complementarity Problems, Edited by R. W. Cottle, F. Giannessi, and J. L. Lions, John Wiley and Sons, Chichester, England, pp. 151–186, 1980.Google Scholar
- 2.Chen, G. Y., and Yang, X. Q., The Complementarity Problems and Their Equivalence with the Weak Minimal Element in Ordered Spaces, Journal of Mathematical Analysis and Applications, Vol. 153, pp. 136–158, 1990.Google Scholar
- 3.Kinderlehrer, D., and Stampacchia, G., An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, NY, 1980.Google Scholar
- 4.Lee, G. M., Kim, D. S., Lee, B. S., and Yen, N. D., Vector Variational Inequality as a Tool for Studying Vector Optimization Problems, Nonlinear Analysis, Vol. 34, pp. 745–765, 1998.Google Scholar
- 5.Yen, N. D., and Lee, G. M., On Monotone and Strongly Monotone Vector Variational Inequalities, Vector Variational Inequalities and Vector Equilibria, Edited by F. Giannessi, Kluwer Academic Publishers, Dordrecht, Netherlands, pp. 467–478, 2000.Google Scholar
- 6.Sawaragi, Y., Nakayama, H., and Tanino, T., Theory of Multiobjective Optimization, Academic Press, New York, NY, 1985.Google Scholar
- 7.Geoffrion, A. M., Proper Efficiency and the Theory of Vector Maximization, Journal of Mathematical Analysis and Applications, Vol. 22, pp. 618–630, 1968.Google Scholar