Linear Regularity and Linear Convergence of Projection-Based Methods for Solving Convex Feasibility Problems
Linear Regularity and Linear Convergence of Projection-Based Methods for Solving Convex Feasibility Problems
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DOI：
10.1007/s00245-017-9417-1
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发表时间：
2017-05
影响因子：
1.8
通讯作者：
Xiaopeng Zhao;K. Ng;Chong Li;J. Yao
中科院分区：
文献类型：
--
作者：
Xiaopeng Zhao;K. Ng;Chong Li;J. Yao
对于Hilbert空间中具有非空交的闭凸集的有限/无限族，研究了凸可行性问题的基于投影的求解方法的（有界）线性正则性和线性收敛性.利用邻点条件和有限余维假设，给出了保证有界线性正则性的几个充分条件。提出了一种求解凸可行性问题的统一投影算法--B-EM算法，并利用有界线性正则性，在引入一种新的控制策略下，证明了该算法的线性收敛性.
For a finite/infinite family of closed convex sets with nonempty intersection in Hilbert space, we consider the (bounded) linear regularity property and the linear convergence property of the projection-based methods for solving the convex feasibility problem. Several sufficient conditions are provided to ensure the bounded linear regularity in terms of the interior-point conditions and some finite codimension assumptions. A unified projection method, called Algorithm B-EMOPP, for solving the convex feasibility problem is proposed, and by using the bounded linear regularity, the linear convergence results for this method are established under a new control strategy introduced here.