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求解带箱式约束全局优化问题的滤子填充函数方法

胡铨1  王薇1,*   

  1. 1. 华东理工大学数学系, 上海 200237
  • 收稿日期:2016-01-08 出版日期:2016-09-15 发布日期:2016-09-15
  • 通讯作者: 王薇 wangwei@ecust.edu.cn
  • 基金资助:

    国家自然科学基金 (Nos. 11271128, 71372113)

A filled function method based on filter for global optimization with box constraints

HU Quan1  WANG Wei1,*   

  1. 1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China
  • Received:2016-01-08 Online:2016-09-15 Published:2016-09-15

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摘要：

提出一个基于滤子技术的填充函数算法, 用于求解带箱式约束的非凸全局优化问题. 填充函数算法是求解全局优化问题的有效方法之一, 而滤子技术以其良好的数值效果广泛应用于局部优化算法中. 为优化填充函数方法, 应用滤子来监控迭代过程. 首先给出一个新的填充函数并讨论了其特性, 在此基础上提出了理论算法及算法性质. 最后列出数值实验结果以说明算法的有效性.

关键词: 箱式约束, 全局优化, 滤子技术, 填充函数

Abstract:

This paper presents a filled function algorithm based on filter technique for the nonconvex global optimization problems with boxed constrains. The filled function method is one of effective methods for solving global optimization problems. And the filter technique is widely used in local optimization algorithm because of its good numerical results. In order to optimize the filled function method, we try to use the filter set to supervise the iteration. In the paper, a new filled function is formulated first and then its necessary characteristics are discussed. Based on that, the algorithm dominated by the filter is proposed and its properties are proved. The numerical results are list at last to show the effectiveness of the algorithm.

Key words: boxed constrains, global optimization, filter technique, filled function