摘要
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.
作者
王霄婷
龙宪军
彭再云
Wang Xiaoting;Long Xianjun;Peng Zaiyun(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China;School of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China)
出处
《计算数学》
CSCD
北大核心
2024年第3期370-384,共15页
Mathematica Numerica Sinica
基金
国家自然科学基金(12271067)
重庆市自然科学基金(CSTB2024NSCQ-MSX1282)
重庆市研究生导师团队建设项目(yds223010)
重庆工商大学研究生创新型科研项目(yjscxx2023-211-187)资助.
关键词
非凸优化
相对光滑
Bregman邻近梯度算法
广义凹KL性质
Nonconvex optimization
Relatively smooth
Bregman proximal gradient algorithm
Generalized concave KL property