一种新的凸组合形式的混合共轭梯度法  

A Hybrid Conjugate Gradient Method as a New Convex Combination

作　　者：陈秀芳 CHEN Xiufang(School of Mathematics and Physics,West Yunnan University,Lincang,Yunnan,China 677000)

机构地区：[1]滇西科技师范学院数理学院,云南临沧677000

出　　处：《昆明学院学报》2023年第3期50-57,共8页Journal of Kunming University

基　　金：云南省教育厅科学研究基金项目(2022J1021);滇西科技师范学院校级科研项目(DXXY202226).

摘　　要：本文提出一种新的混合共轭梯度法来求解无约束优化问题,该方法由文献[13]简记(MHS方法)和Dai-Yuan (DY方法)作凸组合,得到新的共轭参数βkHXF,且凸组合形式下的共轭梯度法产生的搜索方向满足共轭条件,进一步证明该方法不依赖于任何线搜索而满足充分下降性.最后,在一般假设条件下,使用强wolfe线搜索,证明了新算法框架具有全局收敛性.In this paper,a new hybrid conjugate gradient method for constrained optimization problems is presented.This method includes the convex combination of MHS method and Dai Yuan method in reference[13]to obtain new conjugate parametersβHXF k,and the search direction generated by the conjugate gradient method in the form of convex combination meets the conjugate conditions.It is further proved that the method does not rely on any line search and meets the sufficient descent property.Finally,under the general assumptions,strong wolfe line search is used to prove that the new algorithm framework has global convergence.

关 键 词：凸组合 混合共轭梯度法 全局收敛性 充分下降性 

分 类 号：O221.2[理学—运筹学与控制论]