On Monotone and Strongly Monotone Vector Variational Inequalities
By constructing an example we show that the solution sets of a strongly monotone vector variational inequality and of its relaxed inequality can be different from each other. A sufficient condition for the coincidence of these solution sets is given for general vector variational inequalities; connectedness and path-connectedness of the solution sets for some kinds of monotone problems in Hilbert spaces are studied in detail.
Key WordsVector variational inequality monotonicity strong monotonicity solution sets connectedness path-connectedness
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- Brézis H., “Analyse fonctionnelle”. Masson, Paris, 1983.Google Scholar
- Giannessi F., “Theorems of Alternative, Quadratic Programs and Complementarity Problems”. In “Variational Inequality and Complementarity Problems” (Edited by R. W. Cottle, F. Gian-nessi and J.-L. Lions ), Wiley, New York, 1980, pp. 151–186.Google Scholar
- Kinderlehrer D. and G. Stampacchia, “An Introduction to Variational Inequalities and Their Appls.”. Academic Press, New York, 1980.Google Scholar
- Malivert C., “Multicriteria Fractional Programming”. ( Manuscript, September 1996 )Google Scholar
- Rockafellar R.T., “Convex Analysis”. Princeton University Press, Princeton, New Jersey, 1970.Google Scholar
- Steuer R.E., “Multiple Criteria Optimiz.: Theory, Computation and Application”. J. Wiley and Sons, New York, 1986.Google Scholar
- Yen N.D. and Phuong T.D., “Connectedness and Stability of the Solution Sets in Linear Fractional Vector Optimiz. Problems”. This Volume.Google Scholar