强收敛的球松弛CQ算法及其应用

Strongly convergent ball-relaxed CQ algorithm and its application

为了求解分裂可行问题,Yu等提出了一个球松弛CQ算法。由于该算法只需计算到闭球上的投影,同时不需要计算有界线性算子的范数,该算法是容易实现的。但是球松弛CQ算法在无穷维Hilbert空间中仅仅具有弱收敛性。首先构造了一个强收敛的球松弛CQ算法。在较弱的条件下,证明了算法的强收敛性。其次将该算法应用到一类闭凸集上的投影问题上。最后,数值试验验证了该算法的有效性。

In order to solve the split feasibility problem,Yu et al.proposed a ballrelaxed CQ algorithm.Since this algorithm only needs to calculate the projection on the closed balls and does not need to calculate the norm of bounded linear operator,it is easy to implement.But the ball-relaxed CQ algorithm only has weak convergence in infinite dimensional Hilbert spaces.Firstly,a strongly convergent ball-relaxed CQ algorithm is constructed.Under weaker conditions,the strong convergence of the algorithm is proved.Secondly,the algorithm is applied to the projection problem on a class of closed convex sets.Finally,numerical experiments verify the effectiveness of the algorithm.