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On the complex complementarity problem

Published online by Cambridge University Press:  17 April 2009

Bertram Mond
Bertram Mond
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria.
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Abstract

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The complex linear complementarity problem considered here is the following: Find z such that

where S is a polyhedral convex cone in Cp, S* the polar cone, M ∈ Cp×p and q ∈ Cp.

Generalizing earlier results in real and complex space, it is shown that if M satisfies RezHMz ≥ 0 for all z ∈ Cp and if the set satisfying Mz + q ∈ S*, z ∈ S is not empty, then a solution to the complex linear complementarity problem exists. If RezHMz > 0 unless z = 0, then a solution to this problem always exists.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 2 , October 1973 , pp. 249 - 257
Copyright
Copyright © Australian Mathematical Society 1973

References

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