梯度投影法及其Matlab实现

梯度投影法及其Matlab实现(论文9200字)
摘要：最优化理论作为应用数学的一个重要分支，广泛的应用于生活中。梯度投影法作为一种最优化方法，是解决带约束最优化问题的重要手段之一。本文主要研究了梯度投影法概念，性质，在解决实际问题中的应用，并与Zoutendijk可行方向法进行了对比分析，同时通过Matlab软件分别对其进行了实现。最后比较了梯度投影法与Zoutendijk可行方向法的区别与联系。
关键字：最优化理论;梯度投影法; Zoutendijk可行方向法;Matlab

Gradient Projection Method and Its MATLAB program
Abstract: Optimization theory as an important branch of applied mathematics, has been widely used in life. Gradient projection method as an optimization method, is one of the important means to solve optimization problems with constraints. This paper studied the concept, properties, application in solving practical problems of the gradient projection method and had compared with Zoutendijk feasible direction method in theory analysis . Simultaneously, using Matlab made the two algorithms come true and found out the differences and relations between gradient projection method and Zoutendijk feasible direction method.

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Key words: Optimization Theory; gradient projection method; Zoutendijk feasible direction method; Matlab

目 录
摘要    3
1.绪论    5
1.1概述    5
1.2本文所做的工作    5
2.梯度投影法与ZOUTENDIJK 可行方向法的原理及分析    6
2.1  梯度投影法    6
2.2  ZOUTENDIJK可行方向法    11
2.3 梯度投影法与ZOUTENDIJK 可行方向法的对比分析    14
3.梯度投影法与ZOUTENDIJK可行方向法算法思想及其MATLAB实现    16
3.1 梯度投影法算法思想及伪代码实现    16
3.2在不同起始点下，梯度投影法MATLAB程序可靠性检验    23
3.3 ZOUTENDIJK可行方向法算法思想及实现    25
3.4基于MATLAB下的梯度投影法与ZOUTENDIJK可行方向法对比分析    29
4.总结    31
参考文献    31
致谢    32