English

运筹学学报 >

2019 , Vol. 23 >Issue 1: 28 - 34

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2019.01.003

运筹学

求解带箱子集约束的非光滑全局优化问题的填充函数方法

展开
  • 1. 上海第二工业大学理学院, 上海 201209;
    2. 河南科技大学数学与统计学院, 河南洛阳 471003

收稿日期: 2017-11-03

  网络出版日期: 2019-03-15

基金资助

国家自然科学基金（Nos.11471102，11001248，51776116），上海第二工业大学应用数学学科基金（No.A30XK1322100）

收起

Filled function method for solving non-smooth box constrained global optimization problems

Expand
  • 1. College of Science, Shanghai Second Polytechnic University, Shanghai 201209, China;
    2. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, Henan, China

Received date: 2017-11-03

  Online published: 2019-03-15

Fold

摘要

提出了一个求解带箱子集约束的非光滑全局优化问题的填充函数方法.构造的填充函数只包含一个参数，且此参数在迭代过程中容易调节.分析了填充函数的理论性质，在此基础上设计了填充函数算法.数值计算验证了该算法的有效性.

关键词： 非光滑全局优化; 填充函数法; 全局极小点; 非线性方程组

本文引用格式

王伟祥, 尚有林, 王朵 . 求解带箱子集约束的非光滑全局优化问题的填充函数方法[J]. 运筹学学报, 2019 , 23(1) : 28 -34 . DOI: 10.15960/j.cnki.issn.1007-6093.2019.01.003

Abstract

This paper introduces a new filled function method for solving non-smooth box constrained global optimization problems. The constructed filled function contains only one parameter, which could be adjusted readily during the process of the iterations. The theoretical properties of the filled function are analyzed, and a filled function algorithm is designed. Finally, the effectiveness of the proposed algorithm is verified by some numerical calculations.

Key words： non-smooth global optimization; filled function; global optimizer; nonlinear equations

参考文献

[1] Ge R P, Qin Y F. A class of filled functions for finding a global minimizer of a function of several variables[J]. Journal of Optimization Theory and Applications, 1987, 54:241-252.
[2] Zhang L S, Ng C K, Li D. A new filled function method for global optimization[J]. Journal of Global Optimization, 2004, 28:17-43.
[3] Xu Z, Huang H X, Pardalos P M, et al. Filled functions for unconstrained global optimization[J]. Journal of Global Optimization, 2001, 20:49-65.
[4] Wu Z Y, Zhang L S, Teo K L, et al. New modified function for global optimization[J]. Journal of Optimization Theory and Applications, 2005, 125:181-203.
[5] Wu Z Y, Li D, Zhang L S. Global descent methods for unconstrained global optimization[J]. Journal of Global Optimization, 2011, 50:379-396.
[6] Yang Y J, Shang Y L. A new filled function method for unconstrained global optimization[J]. Applied Mathematics and Computation, 2006, 173:501-512.
[7] 孔敏. 一类改进的非光滑规划的填充函数法[J]. 系统科学与数学, 2000, 20:149-154.
[8] 吴青, 刘三阳, 张乐友, 等. 求一类非光滑规划全局极小点的改进的填充函数法[J]. 应用数学, 2004, 17:36-40.
[9] Clarke F H. Nonsmooth analysis and optimization[J]. Proceedings of the International Congress of Mathematicians, 1978, 5:847-853.
[10] Price C J, Robertson B L, Reale M. A hybrid Hooke and Jeeves-Direct method for non-smooth optimization[J]. Advanced Modeling and Optimization, 2008, 11:597-635.
[11] Audet C, Jr J E D. Mesh adaptive direct search algorithms for constrained optimization[J]. SIAM Journal on Optimization, 2006, 17:188-217.
[12] Hoole S R H, Udawalpola R, Wijesinghe K R C. Development of a benchmark problem and a general optimisation package with Powell's method to develop the benchmark[J]. Journal of Materials Processing Technology, 2007, 181:136-141.
[13] Zhang Y, Xu Y, Zhang L. A filled function method applied to nonsmooth constrained global optimization[J]. Journal of Computational and Applied Mathematics, 2009, 232:415-426.
[14] Floudas C A, et al. Handbook of Test Problems in Local and Global Optimization[M]. Kluwer:Acadmic Publishers, 1999.

Options
文章导航

/

〈 〉