2021年论文非线性规划问题.doc

相关非线性计划问题求解

摘 要 ：本文关键探讨求解非线性计划问题两种方法：共轭梯度法和变尺度法.
第一个方法:共轭方向法,是最常见一个方法，共轭梯度法含有结构简单，计算量小，储存量小且结构搜索方向不需要求解线性方程组和算法二次终止性等优点，该方法是最优化方法中相当很好一个方法，尤其是在求解大规模无约束最优化问题时更是得到了广泛应用.
第二种方法：变尺度法，是求解无约束极值问题一个有效方法，，又比梯度法收敛速度快，尤其是对高维问题含有显著优越性，所以使变尺度法取得了很高声誉，至今仍被公认为求解无约束极值问题最有效算法之一.
关键词：非线性计划；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 method commonly 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 非线性计划问题方法 1
1
变尺度法介绍 1
3 共轭梯度法 1
引言 1
基础原理 2
共轭梯度法算法 7
数值试验 7
4 变尺度法 8
8
基础原理 8
计算步骤 9
数值试验 10
结论 13
参考文件 14
致