具有间断扩散性质的线性约束全局优化随机算法

doi:10.15960/j.cnki.issn.1007-6093.2020.01.007

运筹学学报 ›› 2020, Vol. 24 ›› Issue (1): 88-100.doi: 10.15960/j.cnki.issn.1007-6093.2020.01.007

具有间断扩散性质的线性约束全局优化随机算法

陈永¹, 王薇^1,*, 徐以汎²

1. 华东理工大学数学系, 上海 200237;
2. 复旦大学管理学院, 上海 200433

收稿日期:2019-06-19 发布日期:2020-03-09
通讯作者: 王薇 E-mail:wangwei@ecust.edu.cn
基金资助:
国家自然科学基金（No.71531005）

An stochastic algorithm for global optimization with linear constraints based on intermittent diffusion

CHEN Yong¹, WANG Wei^1,*, XU Yifan²

1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China;
2. School of Management, Fudan University, Shanghai 200433, China

Received:2019-06-19 Published:2020-03-09

摘要/Abstract

摘要： 研究带线性约束的非凸全局优化问题，在有效集算法的基础上提出了一个具有间断扩散性质的随机微分方程算法，讨论了算法的理论性质和收敛性，证明了算法以概率收敛到问题的全局最优解，最后列出了数值实验效果.

关键词: 线性约束, 全局优化, 有效集策略, 随机微分方程, 扩散过程

Abstract: In this paper, the nonconvex global optimization problem with linear constraints is studied. Based on the effective set algorithm, a stochastic differential equation algorithm with stochastic diffusion properties is proposed. The theoretical properties and convergence of the algorithm are discussed. It is proved that the algorithm converges to the global optimal solution of the problem with probability 1. Finally, the numerical experiment results are listed.

Key words: linear constraint, global optimization, effective set algorithm, stochastic differential equation, diffusion process

中图分类号:

O221.2

陈永, 王薇, 徐以汎. 具有间断扩散性质的线性约束全局优化随机算法[J]. 运筹学学报, 2020, 24(1): 88-100.

CHEN Yong, WANG Wei, XU Yifan. An stochastic algorithm for global optimization with linear constraints based on intermittent diffusion[J]. Operations Research Transactions, 2020, 24(1): 88-100.

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具有间断扩散性质的线性约束全局优化随机算法

An stochastic algorithm for global optimization with linear constraints based on intermittent diffusion

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