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A note on high degree linear complementarity problems

Published online by Cambridge University Press:  17 April 2009

David E. Stewart
David E. Stewart
Affiliation:
Statistics Department, School of Mathematical Sciences, Australian National University, GPO Box 4 Canberra ACT 2601, Australia
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Abstract

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Topological degree theory can be applied to maps defined from Linear Complementarity Problems, as has been done by Howe and Stone, Ha, and Stewart. It is shown here that the definitions of Howe and Stone, and Stewart, are equivalent. Also a new family of matrices is defined whose degrees' magnitudes increase exponentially as 2n/√2πn, whereas Howe and Stone give examples whose degrees go as (22/5)n.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 1 , February 1992 , pp. 151 - 155
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Ha, C.D., ‘Application of degree theory in stability of the complementarity problem’, Math. Oper. Res. 12 (1987), 368–376.Google Scholar
[2]Howe, R. and Stone, R., ‘Linear complementarity and the degree of mappings’, in Homotopy methods and global convergence, Editors Eaves, B.C., Gould, F.J., Peitgen, H.-O. and Todd, M.J., pp. 179–223 (Plenum Press, New York, London).Google Scholar
[3]Murty, K., ‘On the number of solutions to the complementarity problem and spanning properties of complementary cones’, Linear Algebra Appl. 5 (1972), 65–108.CrossRefGoogle Scholar
[4]Stewart, D.E., ‘A degree theory approach to degeneracy of LCPs’, Linear Algebra Appl. (submited).Google Scholar