求解多集合分裂可行问题的一种改进的投影算法

An Enhanced Projection-type Algorithm for Solving the Multiple-sets Split Feasibility Problem

多集合分裂可行性问题就是要找距一族非空闭凸集最近的点,并且使得其线性变换的像距离另一族非空闭凸集最近。多集合分裂可行性问题是一类重要的最优化问题,产生于工程实践,在信号处理领域中有着广泛的应用。文中给出基于求解分裂可行问题的投影算法,该算法不需要计算矩阵谱半径,并且在迭代过程中,步长的选取不用反复从初始值开始计算,进而减小计算的工作量,提高算法的运算效率。同时该算法具有较好的稳定性,还证明了算法的全局收敛性,并且进行了数值实验,实验结果表明该算法具有较快的收敛速度和良好的可行性。

The multiple-set split feasibility problem is to find the closest point to a family of non-empty closed convex sets in one space,such that its image under a linear transformation will be closest to another family of non-empty closed convex sets in the image space.This multiple-set split feasibility problem is one of the important optimization problems,which generates from the engineering sceneario and is widely applied in the signal processing field.This paper proposes a projection-type algorithm to solve the multiple-set split feasibility problem.It aviods to calculate the spectral radius of the matrix,which can improve the computing efficiency by carefully choosing the stepsize during the iterative process.Additionally it is has a good stable property.The convergence of our algorithm is proved,and valided by the numerical experiments.The results show that the proposed algorithm has a fast convergence rate and good feasibility.