Journal Article10.1017/S0004972700024898
On the complex nonlinear complementary problem
J. Parida,Bijay Kumar Sahoo +1 more
TL;DR: The complex nonlinear complementarity problem considered in this article 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.
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Abstract: 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.
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Citations
Variational Inequality and Complementarity Problem
S. Nanda
- 01 Jan 2011
TL;DR: Variational inequality and complementarity have much in common, but there has been little direct contact between the researchers of these two related fields ofmathematical sciences as discussed by the authors, but there have been few direct contacts between researchers of applied mathematics and operations research.
19
A complex nonlinear complementarity problem
Sribatsa Nanda,Sudarsan Nanda +1 more
TL;DR: In this paper, the authors studied the existence and uniqueness of solutions for the nonlinear complementarity problem, where the mapping g is strongly monotone on S and g is a continuous function from Cn into itself.
Existence theory for the complex nonlinear complementarity problem
J. Parida,B. Sahoo +1 more
TL;DR: The main result in this article is an existence theorem for the following complex nonlinear complementarity problem: find z such that where S is a polyhedral cone in C n, S * the polar cone, and g is a mapping from C n into itself.
On stationary points and the complementarity problem
Sribatsa Nanda,Sudarsan Nanda +1 more
TL;DR: In this article, it was shown that there is a connected set T in S of stationary points of (Dr (e), g) where Dr (e) is the set of all x in S with re(e, x) ≤ r. This extends the results of Lemke and Eaves to complex nonlinear case and arbitrary closed convex cones in Cn.
6
A note on generalised linear complementarity problems
J. Parida,B. Sahoo +1 more
TL;DR: In this article, a new class of matrices, denoted by J -matrices, is introduced and it is shown that for any A in this class, a solution to the generalized linear complementarity problem exists for arbitrary vector q.
2
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TL;DR: In this paper, Frank and Wolfe showed that sp(z) > 0 for all z E C. If M is positive semi-definite (not necessarily syonmetric) and conditions (2) and (3) are consistent, then so are conditions (1)-(3).
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On the complex complementarity problem
TL;DR: In this paper, it was shown that if M satisfies RezHMz ≥ 0 for all z ∈ Cp and if the set satisfying Mz + q ∈ S*, s ∈ P is not empty, then a solution to the complex linear complementarity problem exists.
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