两种带参数的混合共轭梯度算法及其收敛性研究

发布时间：2018-06-17 18:24

本文选题：无约束优化 + 共轭梯度法　；参考：《青岛大学》2017年硕士论文

【摘要】：最优化方法在我们的日常生活中的应用非常广泛。共轭梯度方法是解决大规模无约束优化问题中一种比较重要的方法。本文提出了两种混合的带参数的共轭梯度算法。对这两种算法给出了充分下降性和全局收敛性的证明。第一章介绍了共轭梯度方法的一些基本知识,简要介绍了一些关于共轭梯度方法的发展方向。第二章基于现有的方法,给出了一个带参数的混合共轭梯度算法。这种算法的搜索方向满足充分下降性条件而不依赖于任何线搜索;在使用Wolfe线搜索的情况下具有全局收敛性。数值实验结果表明算法是可行的。第三章构造了一个带参数的三项共轭梯度方法。这一方法的搜索方向同样在不依赖任何线搜索准则的条件下满足充分的下降性条件;在Wolfe线搜索准则条件下这一方法具有全局收敛性。给出的数值算例也表明这种算法是有效的。
[Abstract]:Optimization methods are widely used in our daily life. Conjugate gradient method is an important method for solving large scale unconstrained optimization problems. In this paper, two mixed conjugate gradient algorithms with parameters are proposed. The sufficient descent and global convergence of these two algorithms are proved. In the first chapter, some basic knowledge of conjugate gradient method is introduced, and the development trend of conjugate gradient method is briefly introduced. In chapter 2, a mixed conjugate gradient algorithm with parameters is presented based on the existing methods. The search direction of this algorithm satisfies the sufficient descent condition and does not depend on any line search, and it has global convergence in the case of Wolfe line search. Numerical results show that the algorithm is feasible. In chapter 3, a three-term conjugate gradient method with parameters is constructed. The search direction of this method also satisfies the sufficient descent condition without relying on any line search criteria, and the method has global convergence under Wolfe line search criteria. Numerical examples also show that this algorithm is effective.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O224

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