一种惯性交替极小化算法及其应用  

An inertial alternating minimization algorithm with applications

作　　者：吴双双 唐玉超[1] WU Shuangshuang;TANG Yuchao(Department of Mathematics,Nanchang University,Nanchang,Jiangxi 330031,China)

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（理科版）》2022年第5期481-491,共11页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(12061045,11661056)。

摘　　要：提出一种惯性交替极小化算法求解具有线性等式约束的两块可分离凸极小化问题,其中一块是强凸的。我们证明所提出的算法收敛到原问题和对偶问题最优解。作为应用,将所提出的算法用于求解一类复合凸极小化问题,该问题在图像去噪中有着广泛应用。最后,通过对具有约束的全变分图像去噪模型进行数值实验,数值结果验证所提出算法的有效性和优越性。This paper proposed an inertial alternating minimization algorithm to solve a two-block separable convex minimization problems with linear equality constraints,with one function being strongly convex.It was proved that the proposed algorithm converges to an optimal primal-dual solution of the original problem.The proposed algorithm was applied to solve a class of composite convex minimization problem which was widely used in image denoising.The numerical performance of the proposed algorithm was evaluated on the constrained total variation image denoising model.Numerical results verified the effectiveness and efficiency of the proposed algorithm.

关 键 词：惯性交替极小化算法 强凸函数 全变分 图像去噪. 

分 类 号：O177.92[理学—数学]