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存零约束优化问题的部分罚函数方法

张婷婷1, 李高西1,3, 唐莉萍2, 黄应全1   

  1. 1. 重庆工商大学数学与统计学院, 重庆 400067;
    2. 重庆师范大学数学科学学院, 重庆 401331;
    3. 社会经济应用统计重庆市重点实验室, 重庆 400067
  • 收稿日期:2021-09-22 修回日期:2022-01-06 出版日期:2022-05-25 发布日期:2022-07-23
  • 通讯作者: 李高西,Email:ligaoxicn@126.com.
  • 基金资助:
    国家自然科学基金(11901068,12171060),重庆市基础研究与前沿探索(cstc2019jcyj-msxmX0456,cstc2021jcyj-msxmX0499),重庆工商大学科研项目(1952034,ZDPTTD201908)资助课题.

张婷婷, 李高西, 唐莉萍, 黄应全. 存零约束优化问题的部分罚函数方法[J]. 系统科学与数学, 2022, 42(5): 1234-1245.

ZHANG Tingting, LI Gaoxi, TANG Liping, HUANG Yingquan. Partial Penalty Function Method for Switching Constraints Optimization Problem[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(5): 1234-1245.

Partial Penalty Function Method for Switching Constraints Optimization Problem

ZHANG Tingting1, LI Gaoxi1,3, TANG Liping2, HUANG Yingquan1   

  1. 1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067;
    2. School of Mathematics Sciences, Chongqing Normal University, Chongqing 401331;
    3. Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing 400067
  • Received:2021-09-22 Revised:2022-01-06 Online:2022-05-25 Published:2022-07-23
存零约束优化问题是近年提出的一类新的优化问题,因存零约束的存在,使得常用的约束规范不满足,以至于现有算法的收敛性结果大多不能直接应用于该问题.文章将难处理的存零约束放于目标函数,提出了部分罚函数方法.并证明在存零约束的线性独立约束规范下,罚问题的稳定点序列的聚点为原问题的弱稳定点.同时存在罚问题的局部最优解序列收敛于原问题的任意严格局部最优解.数值结果表明该方法是可行的.
In this paper, the switching-constrained optimization problem is a new optimization problem proposed in recent years. Due to the existence of switchingconstrained, the commonly used constraint qualification is not satisfied, thus, most of the convergence results of existing algorithms cannot be directly applied to this problem. In this paper, we put the difficult switching constraint on the objective function and propose a partial penalty function method. It is proved that under the linear independent constraint qualification with switching constraint, the convergence of the sequence of stable points of the penalty problem is the weak stationary point of the original problem. At the same time, for any strictly local optimal solution of the original problem, there exists a local optimal solution sequence of the penalty problem which converges to it. Finally, numerical results show that the penalty function method is feasible.

MR(2010)主题分类: 

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