基于 MATLAB 的无约束优化问题对称秩－1法与 BFGS 法之探讨

摘要

对称秩－1法和 BFGS 法是用拟牛顿法求解无约束优化问题时最常见的两种方法，它们都具有计算简单、收敛速度快等优点。探讨两种方法的算法格式、收敛速度和计算精度问题，同时利用 MATLAB 软件编程进行实例求解。结果表明：在解的迭代次数和精确度方面，BFGS 算法均明显优于对称秩－1法。%Symmetry rank 1 method (SR - 1) and BFGS algorithm are two kinds of the most common methods in Quasi -Newton optimization ,and the main advantages of them are lower workload and higher convergence rate .This paper compares the effectiveness between SR - 1 and BFGS , discusses the implement program using Matlab software , and analyzes the results by numerical examples . It is found that the BFGS algorithm outperforms the SR -1 method in convergence speed .