求解非凸复合优化问题的惯性Bregman邻近梯度算法

AN INERTIAL BREGMAN PROXIMAL GRADIENT ALGORITHM FOR NONCONVEX COMPOSITE OPTIMIZATION PROBLEMS

本文引入线搜索准则,提出了一种带惯性项的Bregman邻近梯度算法求解一类非凸复合优化问题,其中目标函数为相对光滑的损失函数与非光滑正则函数之和.在广义凹Kurdyka-Łojasiewicz(KL)性质的假设下,证明了算法的全局收敛性.最后将算法应用于图像恢复问题和非凸的l_(1/2)稀疏优化问题,数值实验表明新算法的有效性与优越性.

In this paper,we introduce a line search criterion and propose a Bregman proximal gradient algorithm with a inertial term to solve a class of nonconvex composite optimization problem,where the objective functions are the sum of a relatively smooth loss function and a nonsmooth regular function.Under the assumption of the generalized concave Kurdyka-Łojasiewicz(KL)property,the global convergence of the algorithm is proved.The numerical results on image restoration and nonconvex sparse approximation with l_(1/2) regularization are reported to demonstrate the effectiveness and superiority of the inertial Bregman proximal gradient algorithm.