Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-25T19:47:14.805Z Has data issue: false hasContentIssue false
  • English
  • Français

On the complex nonlinear complementary 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]

Extract

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 complex nonlinear complementarity problem considered here is the following: 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. We study the extent to which the existence of a z ∈ S with g(z) ∈ S* (feasible point) implies the existence of a solution to the nonlinear complementarity problem, and extend, to nonlinear mappings, known results in the linear complementarity problem on positive semi-definite matrices.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 1 , February 1976 , pp. 129 - 136
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Abrams, Robert A., “Nonlinear programming in complex space: sufficient conditions and duality”, J. Math. Anal. Appl. 38 (1972), 619–632.CrossRefGoogle Scholar
[2]Cottle, Richard W., “Note on a fundamental theorem in quadratic programming”, J. Soc. Indust. Appl. Math. 12 (1964), 663–665.CrossRefGoogle Scholar
[3]Hartman, P. and Stampacchia, G., “On some nonlinear elliptic different differential functional equations”, Acta Math. 115 (1966), 271–310.CrossRefGoogle Scholar
[4]McCallum, Charles J. Jr, “Existence theory for the complex linear complementarity problem”, J. Math. Anal. Appl. 40 (1972), 738–762.CrossRefGoogle Scholar
[5]Mond, Bertram, “On the complex complementarity problem”, Bull. Austral. Math. Soc. 9 (1973), 249–257.CrossRefGoogle Scholar
[6]Moré, Jorge J., “Classes of functions and feasibility conditions in nonlinear complementarity problems”, Math. Programming 6 (1974), 327–338.CrossRefGoogle Scholar
[7]Parida, J., “Self-duality in complex mathematical programming”, Cahiers Centre Études Recherche Opér. (to appear).Google Scholar