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A note on generalised linear complementarity problems

Published online by Cambridge University Press:  17 April 2009

J. Parida  and
B. Sahoo
J. Parida
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela, Orissa, India.
B. Sahoo
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela, Orissa, India.
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Abstract

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Given an n × n matrix A, an n-dimensional vector q, and a closed, convex cone S of Rn, the generalized linear complementarity problem considered here is the following: find a z ∈ Rn such that

where s* is the polar cone of S. The existence of a solution to this problem for arbitrary vector q has been established both analytically and constructively for several classes of matrices A. In this note, a new class of matrices, denoted by J, is introduced. A is a J-matrix if

The new class can be seen to be broader than previously studied classes. We analytically show that for any A in this class, a solution to the above problem exists for arbitrary vector q. This is achieved by using a result on variational inequalities.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 2 , April 1978 , pp. 161 - 168
Copyright
Copyright © Australian Mathematical Society 1978

References

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