On Gap Functions for Vector Variational Inequalities
We extend the theory of gap functions for scalar variational inequality problems (see [1,8]) to the case of vector variational inequality. The gap functions for vector variational inequality are defined as set-valued mappings. The significance of the gap function is interpreted in terms of the inverse vector variational inequality. Convexity properties of these set-valued mappings are studied under different assumptions.
Key WordsVector variational inequality gap functions duality Fenchel conjugate
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- Auslander A., “Optimisation: Méthodes Numériques”. Masson, Paris, 1976.Google Scholar
- Chen G.-Y. and Cheng Q.M, “Vector variational inequality and vector Optimization”. Lecture Notes in Econ. and Mathem. Systems, Vol. 285, 1988, pp. 408–416.Google Scholar
- Chen G.-Y. and Yen D., “Equilibrium Problems on a Network with Vector-Valued Cost Functions”. Tech. Paper n. 3.191 ( 717 ) Dept. of Mathem., Univ. of Pisa, Italy, 1992.Google Scholar
- Giannessi F., “Theorems of alternative, quadratic programs and complementarity problems’. In ”Variational Inequality Complementary Problems“ (R.W. Cottle, F. Giannessi, and J.-L. Lions, Eds.), Wiley, New York, 1980, pp. 151–186.Google Scholar
- Giannessi F., “On Minty Variational Principle”. In “New Trends in Mathematical Programming”, Kluwer, 1997, pp. 93–99.Google Scholar
- Isermann H., “Duality in Multi-Objective Linear Programming”. In “Multiple Criteria Problem Solving”, S. Zions (ed.), Springer-Verlag, 1978.Google Scholar
- Jahn J., “Scalarization in Multi-Objective Optimization”. In “Mathematics of Multi-Objective Optimization”, ed. P. Serafini, Springer-Verlag, New York, 1984, pp. 45–88.Google Scholar
- Sawaragi, Y., Nakayama and Tanino, T., “Theory of Multiobjective Optimziation”. Academic Press, New York, 1985.Google Scholar