非凸稀疏正则化的广义条件梯度算法

Generalized Conditional Gradient Algorithm for Non-convex Sparse Regularization

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.