无约束优化二阶曲线法的力学模型及全局收敛性

The Mechanical Models and Global Convergency of the Second Order Curvilinear Methods for Unconstrained Optimization

本文讨论无约束最优化数值方法的二阶曲线方法。首先给出关于一般曲线法的全局收敛性定理及其证明。然后在欧几里得空间ＲＮ中引入力学，给出了ＲＮ中Ｌａｇｒａｎｇｅ运动学方程及其数学上的推导。利用力学概念，给出几个具体的二阶曲线法模型，并给出了它们的全局收敛性分析。

Abstract This paper discusses the second curvilinear methods for unconstrained optimization.We prove the global convergence of the general curvilinear methods. We introduce the mechanics into the Euclideon space RN , and give Lagrange equation of motion. Using the concept of mechanics, we give the models of the second curvilinear methods, and analyze the global convergence properties.