复合凸优化问题的一个非精确多层梯度镜面下降算法  

AN INEXACT GRADIENT MIRROR DESCENT ALGORITHM FOR COMPOSITE CONVEX OPTIMIZATION

作　　者：肖斌 周芷娟 胡清洁[1] Xiao Bin;Zhou Zhijuan;Hu QingJie(School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,桂林541004

出　　处：《数值计算与计算机应用》2021年第4期361-378,共18页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11461015,11761014,11961011);广西自然科学基金(2015GXNSFAA139010,2017GXNSFAA198243)资助.

摘　　要：本文提出一个求解复合凸优化问题的非精确多层梯度镜面下降算法.该算法允许目标函数中光滑部分梯度计算和非光滑部分邻近算子计算都存在误差,在适当条件下分析了该算法函数值误差序列的O(1/k^(2))收敛速度,这里k表示迭代次数.最后关于Lasso问题和Logistic问题的数值结果表明该算法是有效的.In this paper,we present an inexact multilevel gradient mirror descent algorithm for composite convex optimization problem under the presence of the errors of gradient calculations of smooth terms and proximity operator calculations of non-smooth terms.The convergence rate of the proposed algorithm is analyzed under mild conditions.Finally,the algorithm is used to solve the lasso and logistic problems,numerical results show the efficiency of the proposed algorithm.

关 键 词：复合凸优化 邻近梯度算法 非精确多层梯度镜面下降算法 收敛速度 

分 类 号：O224[理学—运筹学与控制论]