Title: Convergence of a Newton-like algorithm solving the nonlinear complementarity problem

Authors: Vyacheslav V. Kalashnikov; Nataliya I. Kalashnykova

Addresses: Tecnológico de Monterrey (ITESM), Campus Monterrey, Av. Eugenio Garza Sada 2501 Sur, Monterrey, Nuevo León, Mexico; Central Economics and Mathematics Institute (CEMI) of the Russian Academy of Sciences, Moscow, Russia; Sumy State University, Sumy, Ukraine ' FCFM, UANL, Cd. Universitaria, San Nicolás de los Garza, Nuevo León, Mexico; Sumy State University, Sumy, Ukraine

Abstract: In the paper, we examine conditions that guarantee the existence of a solution to the parametric nonlinear complementarity problem with a monotone (with respect to x) mapping f: Rⁿ × R^m → Rⁿ and ensure a Newton-like method convergence if the mapping f is strictly monotone and each of its components f_i is a concave function. In addition to that, we prove that the sequence of approximate solutions converges at a quadratic rate.

Keywords: soft data paradigms; Newton-like iterations; parametric complementarity; nonlinear complementarity; convergence properties; knowledge engineering; approximate solutions.

DOI: 10.1504/IJKESDP.2014.069298

International Journal of Knowledge Engineering and Soft Data Paradigms, 2014 Vol.4 No.4, pp.306 - 317

Published online: 09 May 2015 *

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