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Study on Global Convergence Analysis of Some Nonlinear Conjugate Gradient Methods

Author: LiuJinKui
Tutor: WangKaiRong
School: Chongqing University
Course: Operational Research and Cybernetics
Keywords: Nonlinear conjugate gradient method Zoutendijk conditions Wolfe line search Armijo line search Global Convergence
CLC: O224
Type: Master's thesis
Year: 2009
Downloads: 119
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Abstract


The optimization is a wide range of applications , the rapid development of science . It to study a certain mathematical definition of the problem of optimal solution , given the actual problem , a special large-scale problems such as oil exploration , atmospheric modeling , aerospace and other fields , from the many programs select the optimal solution . Conjugate direction method for unconstrained optimization in a common way , between the steepest descent method and Newton method is an effective way . It requires only the use of the first derivative of information , not only to overcome the steepest descent method the slow convergence shortcomings , but also to avoid the second derivative of the Newton method of storage and computing needs . Conjugate direction method generated from research quadratic function minimization , but it can be extended to deal with non- quadratic function minimization problem . This paper studies the conjugate gradient method is a conjugate direction method most commonly used one . It has important practical value in the natural sciences, social sciences , and the actual production , engineering design , and modern management . Concern in recent years , the nonlinear conjugate gradient algorithm exploration results : in PRP, LS method based on two nonlinear conjugate gradient method without any line search can be obtained by the methods of sufficient descent and global convergence of the Wolfe line search . ② combination the the CD method DY method has the advantage to a hybrid nonlinear conjugate gradient method , Wolfe line search of a new method for the decline in global convergence . ③ given in the HS method based on a new nonlinear conjugate gradient method with sufficient descent property and global convergence of this method under the strong Wolfe line search . The ④ given a new nonlinear line search and the global convergence of the PLS method has been in this line search conditions .

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CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Optimization of the mathematical theory
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