最优化方法课程设计--黄金分割法及其算法实现.docVIP

最优化方法课程设计 题 目： 黄金分割法及其算法实现 院 （系）： 数学与计算科学 专 业： 信息与计算科学 课题类型： 验证性 设计性 工综合性 软件开发 2011年 12月 25日 摘 要 最优化理论和方法日益受到重视，已经渗透到生产、管理、商业、军事、决策等各个领域，而最优化模型与方法广泛应用于工业、农业、交通运输、商业、国防、建筑、同学、政府机关等各个部门及各个领域。伴随着计算机技术的高速发展，最优化理论与方法的迅速进步为解决实际最优化问题的软件也在飞速发展。其中，MATLAB软件已经成为最优化领域应用最广的软件之一。有了MATLAB这个强大的计算平台，既可以利用MATLAB优化工具箱（OptimizationToolbox）中的函数，又可以通过算法变成实现相应的最优化计算。 在最优化计算中一维最优化方法是优化设计中最简单、最基本的方法。一维搜索，又称为线性搜索，一维问题是多维问题的基础，在数值方法迭代计算过程中，都要进行一维搜索，也可以把多维问题化为一些一维问题来处理。一维问题的算法好坏，直接影响到最优化问题的求解速度。而黄金分割法是一维搜索方法中重要的方法之一，它适用于任何单峰函数求最小值的问题，甚至于对函数可以不要求连续，是一种基于区间收缩的极小点搜索算法。 关键词：最优化、黄金分割法、MATLAB、算法、一维搜索 Abstract Optimization theory and methods and more attention, have penetrated into the production, management, business, military, decision-making and other fields, and optimization models and methods widely used in industry, agriculture, transportation, commerce, defense, construction, students, government various departments and agencies and other fields. With the rapid development of computer technology, optimization theory and methods for the rapid progress of the optimization problem to solve practical software is also developing rapidly. Which, MATLAB software has become the most optimization software is one of the most widely used. With this powerful computing platform MATLAB, either using MATLAB optimization toolbox (OptimizationToolbox) in the function, but also can achieve the appropriate algorithm to optimize into the calculation. In the calculation of one-dimensional optimization optimization method is to optimize the design of the simplest, most basic method. One-dimensional search, also known as linear search, one-dimensional problem is multi-dimensional problem based on iterative methods in numerical calculation, should be one-dimensional search, can also multi-dimensional problem into a number of one-dimensional problem to deal with. One-dimensional algorithms are directly affected by the speed of