一种新的MBFGS算法
A New MBFGS Algorithm
DOI: 10.12677/AAM.2022.118630, PDF,   
作者: 郑轶天：长沙理工大学数学与统计学院，湖南 长沙
关键词: 非线性搜索；拟牛顿法；全局收敛性；Nonlinear Search； Quasi Newton Method； Global Convergence
摘要: 本文在MBFGS算法的研究基础上，对该算法进行推广，形成了一种新的MBFGS算法。同时，研究了其全局收敛性并给出相关证明。一些数值实验表明，这种改进的MBFGS方法对于给定的测试问题是有效的。对于一些无约束优化问题，新的MBFGS算法平均比单调或传统的非单调格式的BFGS方法使用更少的函数和梯度求值。
Abstract: Based on the research of MBFGS algorithm, this algorithm is extended to form a new MBFGS algo-rithm. At the same time, its convergence is studied and the relevant proof is given. Some numerical experiments show that the improved MBFGS method is effective for a given test problem. For some unconstrained op-timization problems, the new MBFGS algorithm uses less function and gradient evaluation than the mono-tone or traditional non monotone BFGS method.
文章引用：郑轶天. 一种新的MBFGS算法[J]. 应用数学进展, 2022, 11(8): 5981-5985. https://doi.org/10.12677/AAM.2022.118630

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