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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 4067202, 10 pages
https://doi.org/10.1155/2017/4067202
Research Article

A Parameter Perturbation Homotopy Continuation Method for Solving Fixed Point Problems with Both Inequality and Equality Constraints

1School of Mathematics, Luoyang Normal University, Luoyang 471934, China
2Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China
3Section of Mathematics, Aviation University of Air force, Changchun 130022, China
4School of Mathematics, Nankai University, Tianjin 300071, China

Correspondence should be addressed to Menglong Su

Received 9 December 2016; Accepted 23 January 2017; Published 13 February 2017

Academic Editor: Maria L. Gandarias

Copyright © 2017 Menglong Su et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we propose a parameter perturbation homotopy continuation method for solving fixed point problems on more general nonconvex sets with both inequality and equality constraints. By adopting appropriate techniques, we make the initial points not certainly in the set consisting of the equality constraints. This point can improve the computational efficiency greatly when the equality constraints are complex. In addition, we also weaken the assumptions of the previous results in the literature so that the method proposed in this paper can be applied to solve fixed point problems in more general nonconvex sets. Under suitable conditions, we obtain the global convergence of this homotopy continuation method. Moreover, we provide several numerical examples to illustrate the results of this paper.