Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-11T03:39:17.983Z Has data issue: false hasContentIssue false
  • English
  • Français

Existence theory for the complex nonlinear complementarity problem

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The main result in this paper is an existence theorem for the following complex nonlinear complementarity problem: find z such that

where S is a polyhedral cone in Cn, S* the polar cone, and g is a mapping from Cn into itself. It is shown that the above problem has a unique solution if the mapping g is continuous and strongly monotone on the polyhedral cone S.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 3 , June 1976 , pp. 417 - 423
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Karamardian, S., “The nonlinear complementarity problem with applications, part 1”, J. Optimisation Theory Appl. 4 (1969), 87–98.CrossRefGoogle Scholar
[2]Mond, Bertram, “On the complex complementarity problem”, Bull. Austral. Math. Soc. 9 (1973), 249–257.CrossRefGoogle Scholar
[3]Moré, Jorge J., “Coercivity conditions in nonlinear complementarity problems”, SIAM Rev. 16 (1974), 1–16.CrossRefGoogle Scholar
[4]Parida, J. and Sahoo, B., “On the complex nonlinear complementarity problem”, Bull. Austral. Math. Soc. 14 (1976), 129–136.CrossRefGoogle Scholar