A homotopy algorithm for computing the fixed point of selfmapping with inequality and equality constraints
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 selfmapping on general nonconvex 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.
Keywords
 Homotopy method
 general nonconvex sets
 selfmapping
 fixed point.
MSC
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