On the Solutions of Discrete Nonlinear Complementarity and Related Problems

On the Solutions of Discrete Nonlinear Complementarity and Related Problems

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Article ID: iaor200954198
Country: United States
Volume: 33
Issue: 4
Start Page Number: 976
End Page Number: 990
Publication Date: Nov 2008
Journal: Mathematics of Operations Research
Authors:
Keywords: complementarity
Abstract:

This paper concerns the existence of solutions to the discrete nonlinear complementarity problem. The problem is that of finding an integer vector xin the n–dimensional Euclidean space such that both xand f(x) are nonnegative, and the inner product of xand f(x) is equal to zero, where f is a nonlinear function mapping from the n–dimensional Euclidean space into itself. Several sufficient conditions are introduced to show the existence of solutions or a unique solution to the problem. Meanwhile, we study the closely related discrete fixed point problem and provide sufficient conditions for the existence of discrete fixed points. In addition, two economic applications are discussed.

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