论文--非线性规划问题.doc

关于非线性规划问题的求解

摘要:本文主要探讨求解非线性规划问题的两种方法:共轭梯度法和变尺度法.
第一种方法:共轭方向法,是最常用的一种方法,共轭梯度法具有结构简单,计算量小,储存量小且构造搜索方向不需要求解线性方程组以及算法二次终止性等优点,该方法是最优化方法中相当较好的一种方法,特别是在求解大规模无约束最优化问题时更是得到了广泛的应用.
第二种方法:变尺度法,是求解无约束极值问题的一种有效方法,,又比梯度法的收敛速度快,特别是对高维问题具有显著的优越性,因而使变尺度法获得了很高的声誉,至今仍被公认为求解无约束极值问题最有效的算法之一.
关键词:非线性规划;无约束问题;共轭梯度法;变尺度法

About the solution of the nonlinear programming problem


Abstract:This article mainly discuss two methods of solving nonlinear programming problem: conjugate gradient method and variable metric method.
First monly used in the conjugate direction method of a kind of method, the conjugate gradient method has simple structure, small amount of calculation and storage capacity is small and the search direction does not need to solve the linear equations and quadratic termination algorithm, optimization method, this method is quite a good one way, especially in solving large-scale unconstrained optimization problems is more widely used.
The second method is to solve unconstrained extreme value problem of a kind of effective method, variable metric method is developed for nearly 30 years. Because it avoids the calculation of the second derivative matrix and its inverse process, and faster convergence speed than gradient method, especially for high-dimensional problem has significant advantages, thus make the variable metric method won a high reputation, is still recognized as one of the most efficient algorithm solving unconstrained extreme value problem.
Key words:Nonlinear programming;unconstrained problem;conjugate gradient method;the variable metric method
目录
1 绪论 1
2 非线性规划问题的方法 1
1
变尺度法简介 1
3 共轭梯度法 1
引言 1
基本原理 2
共轭梯度法的算法 7
数值实验 7
4 变尺度法 8
8
基本原理 8
计算步骤 9
数值实验 10
结论 13
参考文献 14
致谢 15
1 绪论
非线性规划问题时形成于二十世纪五十年代的新兴学科,(后来称为库恩-塔克条件,又称为K-T条件),典型的应用领域包括预报、生产