一种充分下降的修正PRP三项共轭梯度算法
A Modified PRP Three-Term Conjugate Gradient Algorithm with Sufficient Descent Property
DOI: 10.12677/aam.2024.1310434, PDF,    科研立项经费支持
作者: 刘紫烨*：暨南大学信息科学技术学院，广东 广州；王松华, 赵世安#：百色学院数理科学与统计学院，广西 百色
关键词: 大规模无约束优化；三项共轭梯度；充分下降；全局收敛；Large-Scale Unconstrained Optimization； Three-Term Conjugate Gradient； Sufficient Descent； Global Convergence
摘要: 共轭梯度算法是求解大规模无约束优化问题最有效的方法之一。文章提出一种新型的修正PRP三项共轭梯度算法，该算法具有不依赖任何线搜索充分下降的特点，搜索方向具有信赖域特征。在较为温和条件下，算法全局收敛。数值实验表明，新算法是有效的，比传统PRP三项共轭梯度算法更具竞争力。
Abstract: The conjugate gradient algorithm is one of the most effective methods for solving large-scale unconstrained optimization problems. This paper proposes a novel modified Polak-Ribière-Polyak (PRP) three-term conjugate gradient algorithm, which possesses the characteristic of ensuring sufficient descent without relying on any line search conditions. The search direction of this algorithm exhibits trust region properties. Under relatively mild conditions, the algorithm achieves global convergence. Numerical experiments demonstrate that the new algorithm is effective and more competitive compared to the classical PRP three-term conjugate gradient algorithm.
文章引用：刘紫烨, 王松华, 赵世安. 一种充分下降的修正PRP三项共轭梯度算法[J]. 应用数学进展, 2024, 13(10): 4531-4546. https://doi.org/10.12677/aam.2024.1310434

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