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Jingdong book

最优化计算方法及其MATLAB程序实现

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Jingdong book

最优化计算方法及其MATLAB程序实现

Name: 最优化计算方法及其MATLAB程序实现
Brand: Jingdong book
SKU: 3118192931
Price: 32.15 USD
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Content Description

《最优化计算方法及其MATLAB程序实现》较为系统地介绍了最优化问题的基本理论和方法及其主要算法的MATLAB程序实现。关于无约束最优化问题，主要介绍了线搜索方法、梯度法、牛顿法、共轭梯度法、拟牛顿法、信赖域方法和最小二乘问题的数值解法。关于约束优化问题，主要介绍了最优性条件、线性规划的单纯形方法和非线性规划的可行方向法、罚函数法、二次规划问题和序列二次规划法等。设计的MATLAB程序有精确线搜索的黄金分割法和抛物线法，非精确线搜索的Armijo准则，梯度法，牛顿法，重开始共轭梯度法，BFGS算法，DFP算法，Broyden族方法，信赖域方法，求解非线性最小二乘问题的L－M算法，解约束优化问题的乘子法，求解二次规划的有效集法，SQP子问题的光滑牛顿法以及求解约束优化问题的SQP方法等。此外，书中配有丰富的例题和习题，可供学习者使用。《最优化计算方法及其MATLAB程序实现》既注重计算方法的实用性，又注意保持理论分析的严谨性，强调算法的思想和原理在计算机上的实现。
《最优化计算方法及其MATLAB程序实现》的主要阅读对象是数学与应用数学、信息与计算科学和统计学专业的本科生，应用数学、计算数学和运筹学与控制论专业的研究生，理工科其他有关专业的研究生。对最优化理论与算法感兴趣的教师及科技工作人员。

Catalogue

第1章最优化方法引论
1.1 最优化问题
1.2 向量和矩阵范数
1.3 多元函数分析
1.4 凸集与凸函数
1.5 无约束问题的最优性条件
1.6 无约束优化问题的算法概述
习题1

第2章线搜索方法
2.1 精确线搜索及其MATLAB实现
2.1.1 黄金分割法
2.1.2 抛物线法
2.2 非精确线搜索及其MATLAB实现
2.2.1 Wolfe准则
2.2.2 Armijo准则
2.3 线搜索法的收敛性
习题2

第3章梯度法和牛顿法
3.1 梯度法及其MATLAB实现
3.2 牛顿法及其MATLAB实现
3.3 修正牛顿法及其MATLAB实现
习题3

第4章共轭梯度法
4.1 线性共轭方向法
4.2 线性共轭梯度法及其MATLAB实现
4.3 非线性共轭梯度法及其MATLAB实现
习题4

第5章拟牛顿法
5.1 拟牛顿法及其性质
5.2 BFGS算法及其MATLAB实现
5.3 DFP算法及其MATLAB实现
5.4 Broyden族算法及其MATLAB实现
5.5 拟牛顿法的收敛性
习题5

第6章信赖域方法
6.1 信赖域方法的基本结构
6.2 信赖域方法的收敛性
6.3 信赖域子问题的求解
6.4 信赖域方法的MATLAB实现
习题6

第7章最小二乘问题
7.1 线性最小二乘问题数值解法
7.1.1 满秩线性最小二乘问题
7.1.2 亏秩线性最小二乘问题
7.2 非线性最小二乘问题数值解法
7.2.1 Gauss-Newton法
7.2.2 L-M方法及其MATLAB实现
习题7

第8章最优性条件
8.1 等式约束问题的最优性条件
8.2 不等式约束问题的最优性条件
8.3 一般约束问题的最优性条件
8.4 鞍点和对偶问题
习题8

第9章线性规划问题
9.1 线性规划问题的基本理论
9.2 单纯形法及初始基可行解的确定
9.2.1 线性规划问题的单纯形法
9.2.2 初始基可行解的确定
9.3 线性规划问题的对偶理论
9.4 应用MATLAB求解线性规划问题
习题9

第10章二次规划问题
10.1 等式约束凸二次规划的解法
10.1.1 零空间方法
10.1.2 拉格朗日乘子法及其MATLAB实现
10.2 一般凸二次规划的有效集方法
10.2.1 有效集方法的理论推导
10.2.2 有效集方法的算法步骤
10.2.3 有效集方法的MATLAB实现
习题10

第11章约束优化的可行方向法
11.1 Zoutendijk可行方向法
11.1.1 线性约束下的可行方向法
11.1.2 非线性约束下的可行方向法
11.2 梯度投影法
11.2.1 梯度投影法的理论基础
11.2.2 梯度投影法的计算步骤
11.3 简约梯度法
11.3.1 Wolfe简约梯度法
11.3.2 广义简约梯度法
习题11

第12章约束优化的罚函数法
12.1 外罚函数法
12.2 内点法
12.2.1 不等式约束问题的内点法
12.2.2 一般约束问题的内点法
12.3 乘子法
12.3.1 等式约束问题的乘子法
12.3.2 一般约束问题的乘子法
12.4 乘子法的MATLAB实现
习题12

第13章序列二次规划法
13.1 牛顿一拉格朗日法
13.1.1 牛顿一拉格朗日法的基本理论
13.1.2 牛顿一拉格朗日法的MATLAB实现
13.2 SQP方法的算法模型
13.2.1 基于拉格朗日函数Hesse阵的SQP方法
13.2.2 基于修正Hesse阵的SQP方法
13.3 SQP方法的相关问题
13.3.1 二次规划子问题的Hesse矩阵
13.3.2 价值函数与搜索方向的下降性
13.4 SQP方法的MATLAB实现
13.4.1 SQP子问题的MATLAB实现
13.4.2 SQP方法的MATLAB实现
习题13
参考文献

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