Isotone Projection Cones and Nonlinear Complementarity Problems

A brief introduction of complementarity problems is given. We discuss the notion of *-isotone projection cones and analyze how large is the class of these cones. We show that each generating *-isotone projection cone is superdual. We prove that a simplicial cone in \(R^{m}\) is *-isotone projection cone if and only if it is coisotone (i.e., it is the dual of an isotone projection cone. We consider the solvability of complementarity problems defined by *-isotone projection cones. The problem of finding nonzero solution of these problems is also presented.

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