改进的PRP型谱共轭梯度算法  

Improved PRP-Type Spectral Conjugate Gradient Algorithm

作　　者：林穗华 黄海 LIN Suihua;HUANG Hai(School of Education Science,Guangxi Normal University for Nationalities;College of Mathematics and Computer Science,Guangxi Normal University for Nationalities,Chongzuo Guangxi 532200,China)

机构地区：[1]广西民族师范学院教育科学学院 [2]广西民族师范学院数学与计算机科学学院,广西崇左532200

出　　处：《重庆师范大学学报（自然科学版）》2020年第1期60-67,共8页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11661009);广西高校科研项目(No.ZD2014143);广西民族师范学院科研项目(No.2013RCGG002)。

摘　　要：【目的】研究有效求解二次连续可微无约束优化问题。【方法】设计新的PRP型共轭参数βk^MPRP=gk^T/(‖gk-1‖)^2·(yk-1+2s^T/k-1yk-1/‖sk-1‖^2sk-1)和相应的谱参数公式。【结果】新算法搜索方向自动充分下降且具有信赖域特征,并在一定条件下全局收敛。【结论】数值试验表明该谱共轭梯度算法是有效的。[Purposes]In order to effectively solve the unconstrained optimization problems.[Methods]A modified PRP-type formulas of conjugate parameters βk^MPRP=gk^T/(‖gk-1‖)^2·(yk-1+2s^T/k-1yk-1/‖sk-1‖^2sk-1)and corresponding spectral parameters is proposed.[Findings]The search direction of the new spectral conjugate gradient method automatically possess the sufficient descent properties and trust region characteristics.Moreover,the algorithm converges globally under certain conditions.[Conclusions]The numerical experiments results show that the algorithm is very promising.

关 键 词：无约束优化 谱共轭梯度法 充分下降性 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]