条件梯度法求解非线性分裂可行问题  

Solving Nonlinear Split Feasibility Problem via Conditional Gradient Method

作　　者：宇振盛[1] 王子伦 

机构地区：[1]上海理工大学理学院,上海

出　　处：《应用数学进展》2020年第9期1652-1663,共12页Advances in Applied Mathematics

摘　　要：本文研究了分裂可行问题的条件梯度算法,该算法将求解迭代方向转化成求解一线性子问题,并以线搜索得到的步长作为凸因子,当前方向与上一步迭代点的凸组合作为新的迭代点。算法在迭代的更新步中不使用投影,并且得到的解有较好的稀疏性和低秩性。我们获得了算法的收敛性并给出数值实验对比分析了本文的算法与相关算法在同一算例下的表现情况,得到了良好的结果。In this paper, we consider a conditional gradient algorithm for the split feasibility problem. We get the iterative direction by solving a linear subproblem, use the step size obtained by the line search as the convex factor, and get the new iteration point by the convex combination of the current direction and the previous step iteration point. The algorithm does not use projection in the update step. And the obtained solution has good properties of sparsity and low rank. The numerical experiment compares the performance of the proposed algorithm with other algorithms under the same calculation example.

关 键 词：非线性分裂可行问题 条件梯度法 替代函数 稀疏约束集 IMRT问题 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]