Abstract
The nonlinear complementarity problem is the problem of finding a point x in the n-dimensional Euclidean space,R n, such that x ⩾ 0, f(x) ⩾ 0 and 〈x,f(x)∼ = 0, where f is a nonlinear continuous function fromR n into itself. Many existence theorems for the problem have been established in various ways. The aim of the present paper is to treat them in a unified manner. Eaves's basic theorem of complementarity is generalized, and the generalized theorem is used as a unified framework for several typical existence theorems.
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Kojima, M. A unification of the existence theorems of the nonlinear complementarity problem. Mathematical Programming 9, 257–277 (1975). https://doi.org/10.1007/BF01681350
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DOI: https://doi.org/10.1007/BF01681350