Hostname: page-component-cb9f654ff-h4f6x Total loading time: 0 Render date: 2025-09-02T09:13:55.665Z Has data issue: false hasContentIssue false
  • English
  • Français

A complex nonlinear complementarity problem

Published online by Cambridge University Press:  17 April 2009

Sribatsa Nanda  and
Sudarsan Nanda
Sribatsa Nanda
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela, Orissa, India.
Sudarsan Nanda
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.

In this paper we study the existence and uniqueness of solutions for the following complex nonlinear complementarity problem: find z ∈ S such that g(z) ∈ S* and re(g(z), z) = 0, where S is a closed convex cone in Cn, S* the polar cone, and g is a continuous function from Cn into itself. We show that the existence of a z ∈ S with g(z) ∈ int S* implies the existence of a solution to the nonlinear complementarity problem if g is monotone on S and the solution is unique if g is strictly monotone. We also show that the above problem has a unique solution if the mapping g is strongly monotone on S.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 3 , December 1978 , pp. 437 - 444
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Bazaraa, M.S., Goode, J.J. and Nashed, M.Z., “A nonlinear complementarity problem in mathematical programming in Banach space”, Proc. Amer. Math. Soc. 35 (1972), 165–170.CrossRefGoogle Scholar
[2]Eaves, B.C., “On the basic theorem of complementarity”, Math. Programming 1 (1971), 68–75.CrossRefGoogle Scholar
[3]Habetler, G.J. and Price, A.L., “Existence theory for generalized nonlinear complementarity problems”, J. Optimization Theory Appl. 7 (1971), 223–239.CrossRefGoogle Scholar
[4]Hartman, Philip and Stampacchia, Guido, “On some non-linear elliptic differential-functional equations”, Acta Math. 115 (1966), 271–310.CrossRefGoogle Scholar
[5]Karamardian, S., “Generalized complementarity problem”, J. Optimization Theory Appl. 8 (1971), 161–168.CrossRefGoogle Scholar
[6]Parida, J. and Sahoo, B., “On the complex nonlinear complementary problem”, Bull. Austral. Math. Soc. 14 (1976), 129–136.CrossRefGoogle Scholar
[7]Parida, J. and Sahoo, B., “Existence theory for the complex nonlinear complementarity problem”, Bull. Austral. Math. Soc. 14 (1976), 417–435.CrossRefGoogle Scholar
[8]Parida, J. and Sahoo, B., “On an application of the complex nonlinear complementarity problem”, Bull. Austral. Math. Soc. 15 (1976), 141–148.CrossRefGoogle Scholar