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On stationary points and the 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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Let S be a closed convex cone in Cn, S* the polar cone, g a continuous map from Cn into itself, and e a fixed vector in S*. In this paper we prove that there is a connected set T in S of stationary points of (Dr (e), g) where Dr (e) is the set of all x in S with re(e, x) ≤ r. This extends the results of Lemke and Eaves to the complex nonlinear case and arbitrary closed convex cones in Cn. We show that if g is strictly monotone on S, then T is both unique as well as arcwise connected. This partly solves the open problems raised by Eaves in this more general setting. We also show that if x is a stationary point of (Dr (e), g) and re(e, x) < r then x is a stationary point of (S, g).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 1 , January 1979 , pp. 77 - 86
Copyright
Copyright © Australian Mathematical Society 1979

References

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