# American Institute of Mathematical Sciences

2016, 6(4): 505-519. doi: 10.3934/naco.2016023

## Convergence analysis of a parallel projection algorithm for solving convex feasibility problems

 1 Business School, University of Shanghai for Science and Technology, Shanghai, China 2 Department of Health Services and Outcomes Research, National Healthcare Group, 138543 3 Department of Mathematics and Statistics, Curtin University, Perth,WA 6845

Received  January 2016 Revised  November 2016 Published  December 2016

The convex feasibility problem (CFP) is a classical problem in nonlinear analysis. In this paper, we propose an inertial parallel projection algorithm for solving CFP. Different from the previous algorithms, the proposed method introduces a sequence of parameters and uses the information of last two iterations at each step. To prove its convergence in a simple way, we transform the parallel algorithm to a sequential one in a constructed product space. Preliminary experiments are conducted to demonstrate that the proposed approach converges faster than the general extrapolated algorithms.
Citation: Yazheng Dang, Fanwen Meng, Jie Sun. Convergence analysis of a parallel projection algorithm for solving convex feasibility problems. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 505-519. doi: 10.3934/naco.2016023
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