凸可行问题的块迭代次梯度投影算法(英)

运筹学学报 ›› 2011, Vol. 15 ›› Issue (1): 59-70.

凸可行问题的块迭代次梯度投影算法(英)

党亚峥, 高岩, 支丽平

出版日期:2011-03-15 发布日期:2011-03-15

Block-Iterative Subgradient Projection Algorithms for the Convex Feasibility problem

DANG Ya-Zheng, GAO Yan, ZHI Li-Ping

Online:2011-03-15 Published:2011-03-15

摘要/Abstract

摘要： 本文, 针对由非线性不等式系统构成的凸可行问题，提出了序列块迭代次梯度投影算法和平行块迭代次梯度投影算法. 将非线性不等式系统分成若干个子系统，然后将当前迭代点在子系统各个子集上的次梯度投影的凸组合作为当前迭代点在这个子系统上的近似投影. 在较弱条件下证明了两种算法的收敛性.

Abstract: In this paper, sequential block-iterative subgradient projection algorithm and parallel block-iterative subgradient projection algorithm for solving the convex feasibility problem expressed by the system of inequalities are presented. Each step in these methods consists of finding the approximation projection of the current point on the subsystem which is constructed through parting the system of inequalities into several blocks. The convergence for both of sequential block-iterative subgradient projection algorithm and parallel block-iterative subgradient projection algorithm are obtained under some weak conditions.

党亚峥, 高岩, 支丽平. 凸可行问题的块迭代次梯度投影算法(英)[J]. 运筹学学报, 2011, 15(1): 59-70.

DANG Ya-Zheng, GAO Yan, ZHI Li-Ping. Block-Iterative Subgradient Projection Algorithms for the Convex Feasibility problem[J]. Operations Research Transactions, 2011, 15(1): 59-70.