解凸可行问题的一个带中心技术的外推平行次梯度投影算法

doi:10.13371/j.cnki.chin.q.j.m.2014.01.004

数学季刊 ›› 2014, Vol. 29 ›› Issue (1): 22-29.doi: 10.13371/j.cnki.chin.q.j.m.2014.01.004

解凸可行问题的一个带中心技术的外推平行次梯度投影算法

1. School of Management, University of Shanghai for Science and Technology 2. College of Compiler Science and Technology, Henan Polytechnic University

收稿日期:2013-01-01 出版日期:2014-03-30 发布日期:2022-11-29
作者简介: DANG Ya-zheng(1973-), female, native Xuchang, Henan, an associate professor of Henan Polytechnic University, engages in optimization; HAN Xue-feng(1981-), male native of Puyang, Henan, a lecturer of Henan Polytechnic University, engages in optimization; GAO Yan(1962-), male, native of Wuchang, Heilongjiang, a professor of University of Shanghai for Science and Technology, engages in optimization and control.
基金资助:
Supported by the NNSF of China (11171221)； Supported by the Shanghai Municipal Committee of Science and Technology (10550500800)

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

1. School of Management, University of Shanghai for Science and Technology 2. College of Compiler Science and Technology, Henan Polytechnic University

Received:2013-01-01 Online:2014-03-30 Published:2022-11-29
About author:DANG Ya-zheng(1973-), female, native Xuchang, Henan, an associate professor of Henan Polytechnic University, engages in optimization; HAN Xue-feng(1981-), male native of Puyang, Henan, a lecturer of Henan Polytechnic University, engages in optimization; GAO Yan(1962-), male, native of Wuchang, Heilongjiang, a professor of University of Shanghai for Science and Technology, engages in optimization and control.
Supported by:
Supported by the NNSF of China (11171221)； Supported by the Shanghai Municipal Committee of Science and Technology (10550500800)

摘要/Abstract

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.

关键词:

convex feasibility problem, subgradient; , centering technique, product space, convergence

Abstract: 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.

Key words: convex feasibility problem, subgradient; , centering technique, product space, convergence

中图分类号:

O221

党亚峥, 韩学峰, 高岩 . 解凸可行问题的一个带中心技术的外推平行次梯度投影算法[J]. 数学季刊, 2014, 29(1): 22-29.

DANG Ya-zheng, HAN Xue-feng, GAO Yan. An Extrapolated Parallel Subgradient Projection Algorithm with Centering Technique for the Convex Feasibility Problem[J]. Chinese Quarterly Journal of Mathematics, 2014, 29(1): 22-29.

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解凸可行问题的一个带中心技术的外推平行次梯度投影算法

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

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