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运筹学学报 ›› 2015, Vol. 19 ›› Issue (4): 48-58.doi: 10.15960/j.cnki.issn.1007-6093.2015.04.005

• 运筹学 • 上一篇    下一篇

不等式约束优化一个可行序列线性方程组算法

马国栋1, 简金宝1,*   

  1. 1. 玉林师范学院，广西高校复杂系统优化与大数据处理重点实验室，广西玉林  53700
  • 收稿日期:2014-08-19 出版日期:2015-12-15 发布日期:2015-12-15
  • 通讯作者: 简金宝 jianjb@gxu.edu.cn
  • 基金资助:

    1. 国家自然科学基金(No.11271086);2. 广西自然科学基金(2014GXNSFFA118001);

    3.广西高校科研项目(KY2015YB242);4.广西高校人才小高地创新团队资助项目

A feasible sequential systems of linear equations algorithm for inequality constrained optimization

MA Guodong1, JIAN Jinbao1,*   

  1. 1.Yulin Normal University, Guangxi Colleges and Universities Key Lab of Complex System Optimization and Big Data Processing, Yulin 53700, Guangxi, Chian
  • Received:2014-08-19 Online:2015-12-15 Published:2015-12-15

PDF

490

被引次数

1

摘要：

提出了求解非线性不等式约束优化问题的一个可行序列线性方程组算法. 在每次迭代中, 可行下降方向通过求解两个线性方程组产生, 系数矩阵具有较好的稀疏性. 在较为温和的条件下, 算法具有全局收敛性和强收敛性, 数值试验表明算法是有效的.

关键词: 不等式约束优化, 序列线性方程组算法, 全局收敛性, 强收敛性

Abstract:

In this paper, a feasible sequential systems of linear equations algorithm for inequality constrained optimization is proposed. At each iteration, the proposed algorithm solves only two systems of linear equations with a same coefficient matrix to obtain the feasible descent direction. Furthermore, the sparsity of the coefficient matrix is good. Under some necessary assumptions, the algorithm possesses global and strong convergence. Finally, some preliminary numerical
experiments are reported to show that the algorithm is effective.

Key words: inequality constrained optimization, sequential systems of linear equations algorithm, global convergence, strong convergence