| 摘要: |
| 为高效求解非线性方程组问题，利用凸组合技术设计一个新型搜索方向，同时结合加速线搜索技术，提出一个新的加速FR型共轭梯度算法。在合理的假设下，新算法拥有全局收敛的良好性质。数值试验结果表明，新算法总体上优于经典FR算法和三项FR算法。新算法继承了修正FR方法的良好数值效果、充分下降性及信赖域特征，并具有计算简单和存储量小的特点。 |
| 关键词: 非线性方程组 共轭梯度法 凸组合 充分下降性 全局收敛性 |
| DOI：10.13656/j.cnki.gxkx.20210610.002 |
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| 基金项目:广西自然科学基金项目（2018GXNSFAA281259，2020GXNSFAA159069）和广东财经大学华商学院校内项目（2020HSDS15）资助。 |
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| Accelerated FR Conjugate Gradient Algorithm Based on Convex Combination Technology |
|
LI Dandan1, WANG Songhua2
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| (1.Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou, Guangdong, 511300, China;2.School of Mathematics and Statistics, Baise University, Baise, Guangxi, 533000, China) |
| Abstract: |
| In order to solve the problem of nonlinear equations efficiently,a novel search direction is designed by using convex combination technology.Combined with accelerated line search technology,a new accelerated FR conjugate gradient algorithm is proposed. Under reasonable assumptions,the new algorithm has good properties of global convergence.The numerical results show that the new algorithm is generally superior to the classical FR algorithm and Three-term FR algorithm.The new algorithm inherits the good numerical effect,sufficient descent and trust region characteristics of the modified FR method,and has the characteristics of simple calculation and small storage. |
| Key words: nonlinear equations conjugate gradient method convex combination sufficient descent trait global convergence |
