一个非光滑凸规划问题的可执行束方法（英文）  

An Implementable Bundle Method for Nonsmooth Convex Optimization

作　　者：张清叶 高岩[2] ZHANG Qing-ye;GAO Yan(Department of Basic Courses,Henan Institute of Technology,Xinxiang 453003;School of Management,University of Shanghai for Science and Technology,Shanghai 200093)

机构地区：[1]河南工学院基础部,新乡453003 [2]上海理工大学管理学院,上海200093

出　　处：《工程数学学报》2018年第2期217-232,共16页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11171221);the Natural Science Key Foundation of the Education Department of Anhui Province(KJ2017A402)

摘　　要：本文研究了求解无约束凸规划问题的迫近束方法.首先,我们给出一般束方法.然后,提出迫近参数的一种新的更新策略.在第k次迭代时,如果实际下降量与期望下降量很接近,则扩大迫近参数,反之缩小迫近参数.进而,研究包含次梯度聚集策略和迫近参数更新策略的可执行束方法及其收敛性分析.最后,通过两个数值算例验证了算法的有效性.An implem entable bundle method for unconstrained nonsmooth convex optimization problem is provided in this paper.At first,a general bundle method is given.Next,a new update strategy for the proximal parameter is proposed.At the kyhiteration,if the actual descent is close to the predicted one,the proximal parameter is enlarged;otherwise,it is decreased.Then,an implementable bundle method is proposed,which combines the subgradient aggregation strategy with the proximal parameter update strategy.At the same time,its convergence analysis is given as well.Finally,two numerical examples are presented to show the validity of the algorithm proposed in this paper.

关 键 词：非光滑优化 凸优化 束方法 

分 类 号：O224[理学—运筹学与控制论]