共轭梯度法课程设计.docVIP

最优化方法课程设计报告 题 目： 共轭梯度软件设计 院 （系）： 专 业： 学生姓名： 指导教师： 题目类型： 理论研究 实验研究 工程设计 工程技术研究 软件开发 2010 年 1月 15 日 摘要 共轭梯度法最早是Hestenes和Stiefle（1952）提出来的，用于解正定系数矩阵的线性方程组，在这个基础上，Fletcher和Reeves（1964）首先提出了解非线性最优化问题的共轭梯度法。共轭梯度法是解决无约束非线性最优化问题的重要的方法之一Conjugate gradient method to solve unconstrained nonlinear optimization problem, one of the important ways.），因为共轭梯度法是介于最速下降法与牛顿法之间的一个方法，它仅需利用一阶导数信息，但克服了最速下降法收敛慢的缺点，又避免了牛顿法需要存储和计算Hesse矩阵并求逆的缺点，共轭梯度法不仅是解决大型线性方程组最有用的方法之一，也是解大型非线性最优化最有效的算法一。Mlnf(x)，x∈给出一初始值x1，算法选代产生x2，x3,x4,x 5，…．希望某一是目标函数解或点收敛于解，在我们这次的运筹学课程设计当中我们正是用这种方法要求解最小问题的最优解的。 关键字：共轭梯度法；无约束优化 Abstract Conjugate gradient method was first used by Hestenes and Stiefle (1952) put forward for the solution of positive definite coefficient matrix of linear equations, on this basis, Fletcher and Reeves (1964) first put forward about the problem of nonlinear optimization conjugate gradient method. The conjugate gradient method to solve unconstrained nonlinear optimization problems, one of the important ways, as the conjugate gradient method is between steepest descent method and Newtons method between a method, it requires the use of a first-order derivative information, But the steepest descent method to overcome the shortcomings of slow convergence, but also avoid the need to store and calculate Newtons method and the inverse Hesse matrix of the shortcomings of the conjugate gradient method is not only a large-scale linear equations to solve one of the ways the most useful, but also large-scale solution nonlinear optimization algorithm is the most effective one. Conjugate gradient for the unconstrained optimization problem Mlnf (x), x ∈ given an initial value of x1, the election algorithm is generated on behalf of the x2, x3, x4, x 5, .... Hope that is the objective function of a solution or point of converge