无约束优化的非单调三次正则BB算法

吉林大学学报(理学版) ›› 2019, Vol. 57 ›› Issue (06): 1357-1366.

无约束优化的非单调三次正则BB算法

楚王莉¹, 刘红卫¹, 刘泽显²

1. 西安电子科技大学数学与统计学院, 西安 710126； 2. 中国科学院数学与系统科学研究院, 北京 100190

收稿日期:2019-03-27 出版日期:2019-11-26 发布日期:2019-11-21
通讯作者: 刘泽显 E-mail:liuzexian2008@163.com

Non-monotone Cubic Regularization BB Algorithmfor Unconstrained Optimization

CHU Wangli¹, LIU Hongwei¹, LIU Zexian²

1. School of Mathematics and Statistics, Xidian University, Xi’an 710126, China;
2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Received:2019-03-27 Online:2019-11-26 Published:2019-11-21
Contact: LIU Zexian E-mail:liuzexian2008@163.com

摘要/Abstract

摘要： 先利用BB(BarzilaiBorwein)类型参数构造目标函数Hessian矩阵的近似矩阵, 通过极小化当前迭代点处的三次正则化近似梯度模型求解试探步, 再结合非单调线搜索策略提出一个非单调三次正则BB算法, 最后给出算法的收敛性证明. 数值实验结果表明, 该算法数值性能良好.

关键词: 大规模无约束优化, 梯度算法, BB(BarzilaiBorwein)算法, 三次正则化算法, 非单调线搜索

Abstract: Firstly, a BB(BarzilaiBorwein)type parameter was used to construct the approximate matrix of the Hessian matrix of the objective function, and the trial step was solved by minimizing the cubic regularized approximation gradient model at the current iteration point. Secondly, a nonmonotone cubic regularization BB algorithm was proposed based on nonmonotone line search strategies. Finally, the convergence of the proposed algorithm was proved. Numerical experiment results show that the numerical performance of the algorithm is good.

Key words: 大规模无约束优化, 梯度算法, BB(BarzilaiBorwein)算法, 三次正则化算法, 非单调线搜索

中图分类号:

O221.2

楚王莉, 刘红卫, 刘泽显. 无约束优化的非单调三次正则BB算法[J]. 吉林大学学报(理学版), 2019, 57(06): 1357-1366.

CHU Wangli, LIU Hongwei, LIU Zexian. Non-monotone Cubic Regularization BB Algorithmfor Unconstrained Optimization[J]. Journal of Jilin University Science Edition, 2019, 57(06): 1357-1366.