An Extrapolated Parallel Subgradient Projection Algorithm with Centering Technique for the Convex Feasibility Problem  

作　　者：DANG Ya-zheng HAN Xue-feng GAO Yan 

机构地区：[1]School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China [2]College of Compiler Science and Technology, Henan Polytechnic University, Jiaozho 454000, China

出　　处：《Chinese Quarterly Journal of Mathematics》2014年第1期22-29,共8页数学季刊（英文版）

基　　金：Supported by the NNSF of china(11171221);SuppoSed by the Shanghai Municipal Committee of Science and Technology(10550500800)

摘　　要：In this paper,we present an extrapolated parallel subgradient projection method with the centering technique for the convex feasibility problem,the algorithm improves the convergence by reason of using centering techniques which reduce the oscillation of the corresponding sequence.To prove the convergence in a simply way,we transmit the parallel algorithm in the original space to a sequential one in a newly constructed product space.Thus,the convergence of the parallel algorithm is derived with the help of the sequential one under some suitable conditions.Numerical results show that the new algorithm has better convergence than the existing algorithms.In this paper, we present an extrapolated parallel subgradient projection method with the centering technique for the convex feasibility problem, the algorithm improves the convergence by reason of using centering techniques which reduce the oscillation of the corresponding sequence. To prove the convergence in a simply way, we transmit the parallel algorithm in the original space to a sequential one in a newly constructed product space. Thus, the convergence of the parallel algorithm is derived with the help of the sequential one under some suitable conditions. Numerical results show that the new algorithm has better convergence than the existing algorithms.

关 键 词：convex feasibility problem SUBGRADIENT centering technique product space CONVERGENCE 

分 类 号：O221[理学—运筹学与控制论]