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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (2): 217-232.doi: 10.3969/j.issn.1005-3085.2018.02.008

• • 上一篇    下一篇

一个非光滑凸规划问题的可执行束方法（英）

张清叶1,   高   岩2   

  1. 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
  • 收稿日期:2016-04-15 接受日期:2017-10-11 出版日期:2018-04-15 发布日期:2018-06-15
  • 基金资助:
    国家自然科学基金(11171221)；安徽省教育厅自然科学重点基金(KJ2017A402).

An Implementable Bundle Method for Nonsmooth Convex Optimization

ZHANG Qing-ye1,   GAO Yan2   

  1. 1- Department of Basic Courses, Henan Institute of Technology, Xinxiang 453003 
    2- School of Management, University of Shanghai for Science and Technology, Shanghai 200093
  • Received:2016-04-15 Accepted:2017-10-11 Online:2018-04-15 Published:2018-06-15
  • Supported by:
    The National Natural Science Foundation of China (11171221); the Natural Science Key Foundation of the Education Department of Anhui Province (KJ2017A402).

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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．

关键词: 非光滑优化, 凸优化, 束方法

Abstract: An implementable 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 $k$th iteration, 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.

Key words: nonsmooth optimization, convex programming, bundle method

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