English

运筹学学报 ›› 2015, Vol. 19 ›› Issue (3): 151-160.doi: 10.15960/j.cnki.issn.1007-6093.2015.03.018

• 运筹学 • 上一篇    

约束优化问题的一类光滑罚算法的全局收敛特性

王长钰1, 赵文玲2,*   

  1. 1. 曲阜师范大学管理学院，山东曲阜, 273165; 2. 山东理工大学理学院，山东淄博, 255049
  • 收稿日期:2015-06-06 出版日期:2015-09-15 发布日期:2015-09-15
  • 通讯作者: 赵文玲 zwlsdj@163.com

Global convergence of a class smooth penalty algorithm of constrained optimization problem

WANG Changyu1, ZHAO Wenling2,*   

  1. 1. School of Management, Qufu Normal University,  Shandong Qufu 273165, China; 2. School of Science, Shandong University of Technology, Shandong  Zibo 255049, China
  • Received:2015-06-06 Online:2015-09-15 Published:2015-09-15

PDF

560

被引次数

4

摘要：

对约束优化问题给出了一类光滑罚算法.它是基于一类光滑逼近精确罚函数 l_p(p\in(0,1]) 的光滑函数 L_p 而提出的.在非常弱的条件下, 建立了算法的一个摄动定理, 导出了算法的全局收敛性.特别地, 在广义Mangasarian-Fromovitz约束规范假设下, 证明了当 p=1 时, 算法经过有限步迭代后, 所有迭代点都是原问题的可行解;  p\in(0,1) 时,算法经过有限迭代后, 所有迭代点都是原问题可行解集的内点.

关键词: 精确罚函数, 低阶精确罚函数, 光滑逼近精确罚, 光滑罚算法, 广义Mangasarian-Fromovitz约束规范

Abstract:

For constrained optimization problem, a class of smooth penalty algorithm is proposed. It is put forward based on  L_p , a smooth function of a class of smooth exact penalty function  {l_p}\left( {p\in (0,1]} \right).  Under the very weak condition, a perturbationtheorem of the algorithm is set up. The global convergence of the algorithm is derived. In particular, under the hypothesis of generalized Mangasarian-Fromovitz constraint qualification, it is proved that when p=1 , after finite iterations, all iterative points of the algorithm are feasible solutions of the original problem. When {p \in (0,1)}, after finite iteration, all the iteration points are the interior points of feasible solution set of the original problem.

Key words: The exact penalty function, The lower order exact penalty function, Smooth and exact penalty function approach, Smooth penalty algorithm, The generalized Mangasarian-Fromovitz constraint qualification