求解结构型分裂可行问题的一种交替方向法

AN ALTERNATING DIRECTIONS METHOD FOR STRUCTURED SPLIT FEASIBILITY PROBLEMS

基于结构型分裂可行问题的分离性结构,考虑用交替方向法来求解结构型分裂可行问题.并且给出算法的收敛性说明.提出的新算法不需要在每次迭代过程中计算向集合C的投影,并且可以将高维度的问题转化为低维度的问题.另外初步的数值实验结果表明用此方法是可行且高效的,尤其在时间方面大大的提高了计算效率.

Recently, the alternating directions method has attracted great attention. In this paper we apply alternating directions method for solving structured split feasibility problems. We first reduce the structured split feasibility problem into two smaller scale sub-problems,and then employ alternating directions method to solve them. By this method, instead of computing projection onto the convex set C in every iteration, we only need to compute projections onto simple sets X and Y, which greatly reduces the computational time. The convergence of this method is valid under mild assumptions and its efficiency is also verified by some numerical experiments.