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A complex nonlinear complementarity problem

Published online by Cambridge University Press:  17 April 2009

Sribatsa Nanda  and
Sudarsan Nanda
Sribatsa Nanda
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela, Orissa, India.
Sudarsan Nanda
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela, Orissa, India.
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Abstract

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In this paper we study the existence and uniqueness of solutions for the following complex nonlinear complementarity problem: find z ∈ S such that g(z) ∈ S* and re(g(z), z) = 0, where S is a closed convex cone in Cn, S* the polar cone, and g is a continuous function from Cn into itself. We show that the existence of a z ∈ S with g(z) ∈ int S* implies the existence of a solution to the nonlinear complementarity problem if g is monotone on S and the solution is unique if g is strictly monotone. We also show that the above problem has a unique solution if the mapping g is strongly monotone on S.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 3 , December 1978 , pp. 437 - 444
Copyright
Copyright © Australian Mathematical Society 1979

References

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