非凸非光滑优化问题的两步惯性Bregman邻近交替线性极小化算法  

Two-Step Inertial Bregman Proximal Alternating Linearized Minimization Algorithm for Nonconvex and Nonsmooth Problems

作　　者：赵静[1] 郭晨正 Jing Zhao;Chenzheng Guo(College of Science,Civil Aviation University of China,Tianjin 300300)

机构地区：[1]中国民航大学理学院,天津300300

出　　处：《数学物理学报（A辑）》2024年第6期1630-1651,共22页Acta Mathematica Scientia

基　　金：天津市教委科研计划项目自然科学重点项目(2022ZD007)。

摘　　要：针对一类非凸非光滑不可分优化问题,该文基于邻近交替线性极小化算法,结合两步惯性外推和Bregman距离提出了一种新的迭代算法.通过构造适当的效益函数,利用Kurdyka-Łojasiewicz性质,证明了所提出算法生成的迭代序列具有收敛性.最后,将该算法应用于稀疏非负矩阵分解、信号恢复、二次分式规划问题,通过数值算例表明了提出算法的有效性.In this paper,for solving a class of nonconvex and nonsmooth nonseparable optimization problems,based on proximal alternating linearized minimization method we propose a new iterative algorithm which combines two-step inertial extrapolation and Bregman distance.By constructing appropriate benefit function,with the help of Kurdyka-Łojasiewicz property we establish the convergence of the whole sequence generated by proposed algorithm.We apply the proposed algorithm to solve sparse nonnegative matrix factorization,signal recovery and quadratic fractional programming problems,and show the effectiveness of proposed algorithm.

关 键 词：非凸非光滑优化 邻近交替线性极小化 惯性外推 Bregman 距离 Kurdyka-Łojasiewicz 性质 

分 类 号：O224[理学—运筹学与控制论]