Alternative Theorems for General Complementarity Problems
We describe a method of establishing the existence of solutions to the abstract complementarity problem via convex alternative theorems. The intention is to provide reasonably comprehensive results which rely only on the most central existence theorems for variational inequalities on (weakly) compact sets. The alternative theorem is then applied in several different frameworks.
KeywordsAlternative theorems complementarity problems monotonicity copositivity coercivity P matrices order complementarity
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- Berman A. and Plemmons R.J. “Nonnegative Matrices in the Mathematical Sciences”, New York: Academic Press.Google Scholar
- Borwein J.M. “Norm duality of adjoint processes”, Journal of Optimisation Theory and Applications, to appear.Google Scholar
- Borwein J.M and Dempster M.A.H. “Order complementarity problems in general vector lattices”, Dalhousie Research Report, 1985.Google Scholar
- Borwein J.M and Yost D.A. “Absolute norms on vector lattices”, Proceedings of the Edinburgh Mathematical Society, vol. 27, pp. 215–222, 1984.Google Scholar
- Fan K. “A minimax inequality and applications”, in “Inequalities III” (O. Shisha ed.), New York: Academic Press, 1972.Google Scholar
- Schaeffer H.H. “Banach Lattices and Positive Operators”, Berlin: Springer-Verlag, 1974.Google Scholar