摘要
提出一种具有非凸、非光滑的α‖·‖l1-β‖·‖l21(α>β≥0)罚项的正则化泛函,并且构造了一种新的迭代算法来求解带有αl1-βl2约束的非线性稀疏正则化.该算法利用广义条件梯度算法,将其推广到带有非凸稀疏罚项的非线性正则化方程中,构造出一种适用于非凸稀疏正则化的软阈值算法,并给出了该算法收敛性的证明.
In this paper,a regularized functional with non-convex and non-smoothα‖·‖l1-β‖·‖l2(α>β≥0)penalty is proposed.A new iterative algorithm is constructed to solve theαl1-αl2 constrained nonlinear sparse regularization.The new algorithm is based on the generalized conditional gradient algorithm,the generalized conditional gradient algorithm to the nonlinear regularization equation with non-convex sparse penalty is extended.A soft iterative threshold algorithm for non-convex sparse regularization is proposed and its convergence property is proved.
作者
赵辉
丁亮
Zhao Hui;Ding Liang(Northeast Forestry University)
出处
《哈尔滨师范大学自然科学学报》
CAS
2019年第5期1-6,75,共7页
Natural Science Journal of Harbin Normal University
基金
国家自然科学基金青年基金(41304093)
黑龙江省博士后科研启动基金(LBH-Q16008)
关键词
非线性
非凸
广义条件梯度法
稀疏正则化
不适定问题
Nonlinear
Non-convex
Generalized conditional gradient algorithm
Sparse regularization
Ill posed problem
