无约束优化的修正非单调记忆梯度法

doi:10.3969/j.issn.1000-1565.2018.06.001

河北大学学报(自然科学版) ›› 2018, Vol. 38 ›› Issue (6): 561-566.DOI: 10.3969/j.issn.1000-1565.2018.06.001

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无约束优化的修正非单调记忆梯度法

苏珂,任乐乐,荣自兴,许春

收稿日期:2017-10-17 出版日期:2018-11-25 发布日期:2018-11-25
通讯作者: 任乐乐(1993—),女, 河北张家口人, 河北大学在读硕士研究生.E-mail: 1046176878@qq.com
作者简介:苏珂(1978—),女,河北邯郸人,河北大学教授,博士,主要从事最优化理论和算法的研究. E-mail:suke@hbu.cn
基金资助:
国家自然科学基金资助项目(61572011);河北省自然科学基金资助项目(A2018201172);河北省教育厅重点科研基金资助项目(ZD2015069)

Modified nonmonotone memory gradient method for unconstrained optimization

SU Ke, REN Lele, RONG Zixing, XU Chun

College of Mathematics and Information Science, Hebei University, Baoding 071002, China

Received:2017-10-17 Online:2018-11-25 Published:2018-11-25

摘要/Abstract

摘要： 针对无约束优化问题提出了一种修正的非单调记忆梯度法, 该修正的非单调技术利用前若干个点的凸组合得到一个参照量, 然后将试探点的函数值与该参照量进行灵活比较, 从而决定该试探点是否被接受. 该算法是现有非单调方法的一个推广, 在合理的假设条件下, 得到了算法的全局收敛性. 数值实验结果表明, 该算法是有效且易于实现的.

关键词: 无约束优化, 记忆梯度法, 全局收敛, 非单调

Abstract: A modified nonmonotone line search memory gradient method for unconstrained optimization is proposed in this paper. In this method, a new criterion is constructed to decide whether the trial point is acceptable or not. The presented algorithm is a generalization of the existing nonmonotone-type methods. Under some reasonable conditions, the global convergent properties are proved. The numerical results show that the algorithm is effective and flexible.

Key words: unconstrained optimization, memory gradient methods, global convergence, nonmonotone

中图分类号:

O221.2

苏珂,任乐乐,荣自兴,许春. 无约束优化的修正非单调记忆梯度法[J]. 河北大学学报(自然科学版), 2018, 38(6): 561-566.

SU Ke, REN Lele, RONG Zixing, XU Chun. Modified nonmonotone memory gradient method for unconstrained optimization[J]. Journal of Hebei University (Natural Science Edition), 2018, 38(6): 561-566.

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无约束优化的修正非单调记忆梯度法

Modified nonmonotone memory gradient method for unconstrained optimization

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