最优化课程设计

《最优化》课程设计

题 目：牛顿法与阻尼牛顿法算法分析 学 院: 数学与计算科学学院 专 业： 数学与应用数学 姓名学号： 廖丽红 1000730105

欧 艳 1000730107 骆宗元 1000730122 沈琼赞 1000730127

指导教师： 李向利

日 期：2012年11月08日

最优化课程设计

摘 要

本文基于阻尼牛顿法在解决无约束最优化问题中的重要性，对其原理与算法予以讨论。论文主要是参阅大量数学分析和最优化理论方法，还有最优化方法课程以及一些学术资料，结合自己在平时学习中掌握的知识，并在指导老师的建议下，拓展叙述牛顿法和其改进方法——阻尼牛顿法的优缺点，同时针对阻尼牛顿法的基本思路和原理进行研究，其搜索方向为负梯度方向，改善了牛顿法的缺点，保证了下降方向。

关键词：无约束 牛顿法 下降方向 阻尼牛顿法 最优解

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最优化课程设计

Abstract

This thesis is based on the importance of the damping Newton's method to solve unconstrained optimization problems, we give the discussion about its principles and algorithms. We search a large number of mathematical analysis and optimization theory methods, optimization methods courses, as well as some academic information ,and at the same time combined with knowledge we have learning in peacetime and thanks to the instructor's advice, we also give an expanding narrative for the Newton's method and the improved method -- damping Newton method's advantages and disadvantages, and make a study of the basic ideas and principles for damping Newton method at the same time , we find that a negative gradient direction is for the search direction of the damping Newton method, this method improves the shortcomings of the Newton method which can ensure the descent direction.

Keywords: unconstrained , Newton's method , descent direction ,

damping Newton's method ,optimal solution

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