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Isotone projection cones in Hilbert spaces and the complementarity problem. (English) Zbl 0719.46011
Summary: One defines and studies the concept of isotone projection cone in a Hilbert space H. The isotone projection cone is a closed and convex cone $$K\subset H$$ such that the metric projection $$P_ k$$ is isotone with respect to the order defined by K. One gives some applications to the study of the complementarity problem.

##### MSC:
 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 91A99 Game theory 49J99 Existence theories in calculus of variations and optimal control