Optimization - II -
西南交通大学 数学学院 信息与计算科学 2012
目录
一 问题描述及分析 ································································································ ··················································· 2
1.1 问题重述 ································································································ ······················································ 2
1.2 问题凸性质的分析 ································································ ······································································ 3
1.3 问题解情况的分析 ································································ ······································································ 4
1.4 问题求解 ································································································································ ····················· 4
二 线性搜索 ································································································ ······························································· 4
2.1 精确线搜索——黄金分割法 ································································ ······················································ 4
2.2 非精确线搜索——Armijo 型 ································································································ ····················· 5
三 下降方法 ································································································ ······························································· 6
3.1 最速下降法 ································································································ ·················································· 7
3.2 牛顿法 ································································································ ·························································· 8
3.3 拟牛顿法 —— BFGS ································································ ·································································· 8
四 解线性方程组 ································································································ ······················································· 9
五 Matlab 编程实践 ································································ ················································································ 10
5.1 电脑配置 ································································································································ ···················· 10
5.2 求解方案 ································································································································ ··················· 10
5.3 案例及计算结果 ································································································································ ······· 10
5.4 案例的结果中的方法对比 ································································································ ························ 11
六 实验小结和备忘 ································································································ ················································· 12
七 参考文献 ································································································ ····························································· 13
一 问题描述及分析
在通过编程解决我们所要面对的问题之前,我们首先叙述我们所要解决的问题,并作一些
基本的分析。
1.1 问题重述
求解下面带简单约束的优化问题(或者可以看作是无约束的问题)
(1.1)
其中、、作为待定参数。
为了方便,令