一个具有n步二次收敛性的直接法算法

A DIRECT ALGORITHM WITH n-STEP QUADRATIC CONVERGENCE

在非线性最优化的直接法算法中,Powell 算法具有一定的代表性,但我们已知Powell 算法对正定二次函数一般不具有二次终结性,为此围绕着改善 Powell 算法的算法特性,出现了一系列 Powell 算法的改进型.其中俞文(鱼此)教授提出了一个新的方法——PY 算法,其基本思想基于。

A modifiel PY method is proposed.Its main character is that the rotation transformationand Gram-Schmidt orthogonalizing process are used to rectify the set of search directions.Hence,the algorithm remains not only the quadratic termination,but also the n-step quardra-tic convergence for the objective function which is uniform convex.