摘要
提出一个简单的原始-对偶算法求解三个凸函数之和的最小化问题,其中目标函数包含有梯度李普希兹连续的光滑函数,非光滑函数和含有复合算子的非光滑函数.在新方法中,对偶变量迭代使用预估-矫正的方案.分析了算法的收敛性和收敛速率.最后,数值实验说明了算法的有效性.
In this study, we propose a simple primal-dual algorithm for minimization of a sum of three convex separable functions, which are involved a smooth function with Lipschitz continuous gradient, a nonsmooth function and a linear composite nonsmooth function. A predictor-corrector scheme to the dual variable is used in our algorithm.Convergence and convergence rate are also discussed. In the end, numerical results illustrate the efficiency of this method.
作者
王硕
朱志斌
张本鑫
WANG Shuo1, ZHU Zhibin1, ZHANG Benxin2(1. School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, Guangxi, China;2. School of Electronic Engineering and Automation, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments, Guilin University of Electronic Technology, Guilin 541004, Guangxi, Chin)
出处
《运筹学学报》
CSCD
北大核心
2018年第2期127-138,共12页
Operations Research Transactions
基金
国家自然科学基金(Nos.11361018,11461015)
广西自然科学基金(No.2014GXNSFFA118001)
广西密码学与信息安全重点实验室基金(No.GCIS201624)
广西自动检测技术与仪器重点实验室基金(No.YQ18107)
广西研究生教育创新计划项目(No.YCSW2018141)
关键词
原始-对偶方法
鞍点问题
全变分
图像重建
primal-dual method
saddle-point problem
total variation
image recon-struction
