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Minimising quadratic functionals over closed convex cones

Published online by Cambridge University Press:  17 April 2009

M. Seetharama Gowda
M. Seetharama Gowda
Affiliation:
Department of Mathematics, University of Maryland, Baltimore County, Catonsville, Maryland 21228, Unites States of America
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Abstract

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In this article we show that, under suitable conditions a quadratic functional attains its minimum on a closed convex cone (in a finite dimensional real Hilbert space) whenever it is bounded below on the cone. As an application, we solve Generalised Linear Complementarity Problems over closed convex cones.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 1 , February 1989 , pp. 15 - 20
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Frank, M. and Wolfe, P., ‘An alogorithm for Quadratic Programming’, Naval Res. Logist. Quart. 3 (1956), 95–110.Google Scholar
[2]Gowda, M. Seetharama and Seidman, T.I., ‘Generalized Linear Complementarity Problems’, UMBC Research Report September 1985, Math. Programming (to appear).Google Scholar
[3]McCallum, C.J. Jr., ‘Existence Theory for the Complex Linear Complementarity Problem’, J. Math. Anal. Appl. 40 (1972), 738–762.CrossRefGoogle Scholar
[4]Perold, A.F., ‘A Generalization of the Frank-Wolfe Theorem’, Math. Programming 18 (1980), 215–227.Google Scholar