求解分裂可行问题的一种投影算法

A Projection-type Method to Solve the Split Feasibility Problem

分裂可行问题产生于工程实践,在信号处理领域有广泛的应用。基于求解线性变分不等式的投影方法,设计了一类求解分裂可行问题的新的投影算法。通过约束最优化问题与变分不等式问题的等价性理论进行问题转化。该算法不需计算矩阵逆和矩阵最大特征值,具有较好的稳定性。还证明了该算法的全局收敛性并进行了数值实验,实验结果表明该方法具有较快的收敛速度和良好的可行性。

The split feasibility problem stems from engineering practice and has important applications in signal processing. Based on the projection-type methods to solve the linear variational inequalities, a new projection-type algorithm is designed to solve the split feasibility problem. Considering the theoretical equivalence of constrained optimization problem and variational inequality problem, the former problem can be transformed to the latter. The new algorithm needs not calculate the inverse matrix and the maximal eigenvalue of the matrix . The algorithm is stable. Numerical experiments are conducted to prove the convergence of the method. The results have shown that the method converges fast and can be applied easily.