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On an application of 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.
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Abstract

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A theorem on the existence of a solution under feasibility assumptions to a convex minimization problem over polyhedral cones in complex space is given by using the fact that the problem of solving a convex minimization program naturally leads to the consideration of the following nonlinear complementarity problem: given g: Cn → Cn, find z such that g(z) ∈ S*, z ∈ S, and Re〈g(z), z〉 = 0, where S is a polyhedral cone and S* its polar.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 1 , August 1976 , pp. 141 - 148
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Frank, Marguerite and Wolfe, Philip, “An algorithm for quadratic programming”, Naval Res. Log. Quart. 3 (1956), 95–110.CrossRefGoogle Scholar
[2]Kojima, Masakazu, “A unification of the existence theorems of the nonlinear complementarity problem”, Math. ProgranmLng 9 (1975), 257–277.CrossRefGoogle Scholar
[3]McCallum, Charles J. Jr, “Existence theory for the complex linear complementarity problem”, J. Math. Anal. Appl. 40 (1972), 738–762.CrossRefGoogle Scholar
[4]Parida, J., “On converse duality in complex nonlinear programming”, Bull. Austral. Math. Soc. 13 (1975), 421–427.CrossRefGoogle Scholar
[5]Parida, J. and Sahoo, B., “On the complex nonlinear complementarity problem”, Bull. Austral. Math. Soc. 14 (1976), 129–136.CrossRefGoogle Scholar
[6]Parida, J. and Sahoo, B., “Existence theory for the complex nonlinear complementarity problem”, Bull. Austral. Math. Soc. 14 (1976), 417–423.CrossRefGoogle Scholar