一种部分非精确求解可分离凸优化问题的渐近点算法
A partial inexact proximal point method for separable convex programming
作者：陈小彪(太原工业学院理学系，太原 030008)；李耿华(重庆大学数学与统计学院,重庆 401331)；张玫玉(重庆大学数学与统计学院,重庆 401331)
Author：CHEN Xiao-Biao(Science Department,Taiyuan Institute of Technology, Taiyuan 030008, China)；LI Geng-Hua(College of Mathematical and Statistics, Chongqing University, Chongqing 401331, China)；ZHANG Mei-Yu(College of Mathematical and Statistics, Chongqing University, Chongqing 401331, China)
收稿日期：2017-12-12 年卷（期）页码：2019,56(1):8-12
期刊名称：四川大学学报: 自然科学版
Journal Name：Journal of Sichuan University (Natural Science Edition)
关键字：凸优化问题; 结构型变分不等式; 交替方向法; 渐近点算法; 预测-校正步法
Key words：Convex programming; Structured variational inequality; Alternating direction method; Proximal point method; Prediction-correction method
基金项目：太原工学院青年基金（2015LQ16）
中文摘要
本文研究了一类具有可分离结构的凸优化问题，在经典的交替方向法的基础上得到了一种部分非精确的渐近点算法.该方法分别求解凸优化问题的两个子问题，其中一个直接求解，另一个通过引入非精确项降低了求解的难度. 在合理的假设下，新算法的收敛性得到了证明。数值实验表明新算法是有效的.
英文摘要
In this paper, a new method is proposed for solving a class of separable convex programming problem. The method is referred to as the partial inexact proximal point method. In the method, we take a fresh look at the alternating direction method of multipliers and two sub-problems are solved independently. One is solved directly and the other is handled by bring in inexact minimization. Convergence of the method is proved under mild assumptions and its efficiency is also verified by numerical experiments.
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