可行方向法的统一探讨:二阶段算法模型

A Unified Approach to the Feasible Direction Methods: A Two-Stage Algorithm Model

1 引言可行方向法是非线性规划中一类思想简单数值效果好的基本方法。特别是对线性约束问题,这类方法一直受人欢迎。但由于非线性约束带来的困难,这一领域内的工作近年来并不多见。文[1]曾统一和推广了国内外文献中常见的投影梯度和既约梯度法。本文首先提出一个二阶段算法模型用来解不等式约束问题,大范围地统一和推广了现有的可行方向法。然后,对于一般非线性规划问题,本文利用仅含等式约束的Lagrange函数作为搜索函数,直接应用上述模型的结果给出相应的模型,大大推广和简化了[2]中方法。

This paper presents a two-stage feasible direction algorithm model for nonlinear constrained optimization, in which the results in papers [1,2,3] are combined with the features of the search directions determined by common feasible direction methods, Hence the common feasible direction methods are extended and unified, and the global convergence of the algorithm model is proved under very weak conditions. The model is. simple in form and can be applied easily.