分裂可行问题的一个强收敛算法

A Strongly Convergent Algorithm for the Split Feasibility Problem

分裂可行问题是一类应用很广泛的最优化问题。经典的CQ算法仅具有弱收敛性。为了得到强收敛性,本文通过改进文献中的算法,构造了一个具有强收敛性的算法。该算法为了避免计算有界线性算子的范数,还采用了变步长策略。并且在较弱的条件下,证明了算法的强收敛性。

The split feasibility problem is a kind of widely used optimization problem. The classical CQ algorithm only has weak convergence. In order to obtain strong convergence, this paper constructs an algorithm with strong convergence by improving the algorithms in the literature. In order to avoid calculating the norm of the bounded linear operator, the algorithm also adopts the strategy of variable step size. Under the weaker condition, the strong convergence of the algorithm is proved.