A homotopy algorithm for computing the fixed point of self-mapping with inequality and equality constraints

Volume 9, Issue 6, pp 4888--4896 http://dx.doi.org/10.22436/jnsa.009.06.124

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Authors

Zhichuan Zhu - Faculty of Statistics, Jilin University of Finance and Economics, Changchun, Jilin 130117, China. - School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China. Yang Li - School of Computer Science and Engineering, Changchun University of Technology, Changchun 130012, China. Yanchun Xing - Faculty of Statistics, Jilin University of Finance and Economics, Changchun, Jilin 130117, China. Xiaoyin Wang - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China.

Abstract

In this paper, to compute the fixed point of self-mapping on general non-convex sets, a modified constraint shifting homotopy algorithm for perturbing simultaneously both equality constraints and inequality constraints is proposed and the global convergence of the smooth homotopy pathways is proven under some mild conditions. The advantage of the newly constructed homotopy is that the initial point needs to be only in the shifted feasible set, not necessarily, an interior point in the original feasible set, and hence it is more convenient to be implemented than the existing results. Some numerical examples are also given to show its feasibility and effectiveness.

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Keywords

• Homotopy method
• general non-convex sets
• self-mapping
• fixed point.

MSC

•  90C33
•  65H10

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