一个求解无约束优化问题的无线有哪些信誉好的足球投注网站技术共轭梯度路径法.docVIP

一个求解无约束优化问题的无线有哪些信誉好的足球投注网站技术共 轭梯度路径法 王珏钰1，朱德通2 1 上海师范大学数理学院，上海　200234 2 上海师范大学商学院，上海　200234 摘要：提出一种新的解无约束优化问题的离散共轭梯度路径法. 共轭梯度路径通过构造目标函 数的二次模型来获得. 在合理的假设条件下，证明了算法的整体收敛性和局部超线性或者二次 收敛速率，数值结果表明了算法的有效性． 关键词：运筹学与控制论; 共轭梯度法; 无约束优化; 全局收敛性; 非单调技术. 中图分类号： O224 A Conjugate Gradient Path Method without Line Search Technique for Unconstrained Optimization WANG Jue-Yu1, ZHU De-Tong2 1 Department of Mathematics and Sciences, University of Normal, Shanghai 200234 2 Department of Business, University of Normal, Shanghai 200234 Abstract: In this paper, we propose a new approach via discrete conjugate gradient path for solving unconstrained optimization. The conjugate gradient path is obtained by constructing quadratic model of the objective function. The global convergence and local quadratic or superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, the numerical results are reported to show the e?ectiveness of the proposed algorithm. Key words: Operations research and control theory; Conjugate Gradient Method; Unconstrained Optimization; Global Convergence; Nonmonotonic Technique. 基金项目： the National Natural Science Foundation ，the Chinese Education Ministry Ph.D. Foun- dation (2009312711005) 作者简介： Wang Jue-yu (1973-），male，graduate student，major research direction：Optimization theory and methods. Correspondence author：Zhu De-tong（1954-），male，professor，major research direction：Optimization theory and methods. -1- 0  Introduction In this paper we consider the solution of the unconstrained optimization problem: min f(x), x  x ∈  n  (1) where f :  n  →  is a smooth nonlinear function and x ∈  n  is a real vector with n ≥ 1 components. The conjugate gradient method is implemented via the construction of an orthogonal basis for the underlying Krylov subspace. The idea of quadratic forms is introduced and used to derive the methods of conjugate gradients. We consider the quadratic model ?k of the objectiv