摘要
The purpose of this paper is to apply inertial technique to string averaging projection method and block-iterative projection method in order to get two accelerated projection algorithms for solving convex feasibility problem.Compared with the existing accelerated methods for solving the problem,the inertial technique employs a parameter sequence and two previous iterations to get the next iteration and hence improves the flexibility of the algorithm.Theoretical asymptotic convergence results are presented under some suitable conditions.Numerical simulations illustrate that the new methods have better convergence than the general projection methods.The presented algorithms are inspired by the inertial proximal point algorithm for finding zeros of a maximal monotone operator.
The purpose of this paper is to apply inertial technique to string averaging projection method and block-iterative projection method in order to get two accelerated projection algorithms for solving convex feasibility problem.Compared with the existing accelerated methods for solving the problem,the inertial technique employs a parameter sequence and two previous iterations to get the next iteration and hence improves the flexibility of the algorithm.Theoretical asymptotic convergence results are presented under some suitable conditions.Numerical simulations illustrate that the new methods have better convergence than the general projection methods.The presented algorithms are inspired by the inertial proximal point algorithm for finding zeros of a maximal monotone operator.
基金
supported by the National Natural Science Foundation of China (11171221)
Shanghai Municipal Committee of Science and Technology (10550500800)
Basic and Frontier Research Program of Science and Technology Department of Henan Province (112300410277,082300440150)
China Coal Industry Association Scientific and Technical Guidance to Project (MTKJ-2011-403)
作者简介
Corresponding author.Yazlleng Dang was born in 1973. She received the M.S. degree from Henan Polytechnic University in 2007 and Ph.D. degree from School of Management, University of Shanghai for Science and Technology. Her main research interests include systems engineering and nonsmooth optimization. E-mail： jgdyz@ 163.comYah Gao was born in 1962. He received his Ph.D. degree from Dalian University of Technology in 1996. Now He is a professor of University of Shanghai for Science and Technology. He has published 150 journal papers, and authored 2 books. His research interests include nonsmooth optimization, systems engineering and control theory.E-mail： gaoyan@usst.edu.comLihua Li was born in 1979. She received the M.S. degree from East China Normal University in 2004. Now she is a Ph.D. candidate in School of Management, University of Shanghai for Science and Technology. Her main research interests include system optimization and control. E-mail： llh@ shiep.edu.cn
