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一种具有充分下降性的修正DL型谱共轭梯度法

2023-09-06李亚敏

浙江理工大学学报 2023年4期

摘 要: 提出了一种大规模无约束优化问题的求解方法,通过修正Dai-Liao(DL)共轭梯度法的共轭参数和谱共轭梯度法的谱参数,构造了一种修正DL型谱共轭梯度法。所选取的谱参数使得每次迭代都自动产生一个不依赖于任何线搜索的下降方向;在常规假设下,利用强Wolfe线搜索证明了此方法对一致凸函数是全局收敛的。

关键词: 无约束优化;强Wolfe线搜索;谱共轭梯度法;谱参数;全局收敛

中图分类号: O221.2 文献标志码: A 文章编号: 1673-3851 (2023) 03-0279-06

引文格式:李亚敏.一种具有充分下降性的修正DL型谱共轭梯度法[J]. 浙江理工大学学报(自然科学),2023,49(2):279-284.

Reference Format: LI Yamin. A modified DL-type spectral conjugate gradient method with sufficiently descent property[J]. Journal of Zhejiang Sci-Tech University,2023,49(2):279-284.

A modified DL-type spectral conjugate gradient method with sufficiently descent property

LI Yamin

(School of Economics, Technology & Media University of Henan Kaifeng, Kaifeng 475001, China)

Abstract:  A method for solving large-scale unconstrained optimization problems is proposed. By modifying the conjugate parameter of the Dai-Liao (DL) conjugate gradient method and the spectral parameter of the spectral conjugate gradient method, a modified DL-type spectral conjugate gradient method is constructed. The spectral parameter is selected so that each iteration automatically generates a descent direction that does not depend on any line search. Under conventional assumptions, it is proved that this method is globally convergent for uniformly convex functions by using strong Wolfe line search.

Key words: unconstrained optimization; strong Wolfe line search; spectral conjugate gradient method; spectral parameter; global convergence

0 引 言

共軛梯度法(Conjugate gradient method, CGM)的迭代格式简单,在计算时仅需要目标函数值和梯度函数值,无需计算二阶导数值,储存需求低,是求解无约束优化问题(1)的常用迭代方法之一:

3 结 论

本文在DL法和谱共轭梯度法的基础上,把DL法的共轭参数βDLk的第一项gTkyk-1dTk-1yk-1修正为gTk(gk-gk-1)‖dk-1‖2,得到了共轭参数βDL-Rk=gTk(gk-gk-1)‖dk-1‖2-tgTksk-1dTk-1(gk-gk-1),修正谱参数为θk=1+βDL-RkgTkdk-1‖gk‖2,使得搜索方向dk不依赖于任何线搜索都充分下降,进而得到了一种求解大规模无约束优化问题的修正DL型谱共轭梯度法;并在强Wolfe线搜索下证明了该方法对一致凸函数是全局收敛的。

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(责任编辑:康 锋)

收稿日期: 2022-08-01网络出版日期:2022-11-01网络出版日期

作者简介: 李亚敏(1992- ),女,河南开封人,助教,硕士,主要从事优化理论方面的研究。