幾種非線性共軛梯度法的算法研究及全局收斂性分析.pdf

1、重慶大學(xué)碩士學(xué)位論文幾種非線性共軛梯度法的算法研究及全局收斂性分析姓名：曹偉申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：王開榮2010-04重慶大學(xué)碩士學(xué)位論文 英文摘要 II ABSTRACT Optimization is usually divided into two types of unconstrained and constrained. This paper focuses on the transformati

2、on to analysis the constrained optimal problem.Unconstrained optimization is the main base and effective way of the optimization. Nonlinear conjugate gradient algorithm is a common and effective algorithm, which can

3、 slove most of the problem of the large-scale unconstrained effectively. Whether in social science，natural science, production practice, or in the modern management, nonlinear conjugate gradient algorithm has been widel

4、y applied. This topic based on the research results from home and abroad. After careful analysis, elaboration, and validation, through selecting proper search criteria, improving parameters k β , and constructing a new

5、search direction k d , to get the new algorithm. The new method inherits the achievements of predecessors, moreover, with the extensions for it . This paper studies several nonlinear conjugate gradient algorithms, which

6、 obtained in dissertation may be summarized as follows： 1. The PRP method is generally believed to be the most efficient conjugate gradient method recently. The new PRP algorithm which has sufficiently descending propert

7、y, and the new search direction can keep in a trust region automatically without carrying out any linear search rule. What is more, this algorithm possesses are superior to convergence property for nonconvex function and

8、 uniformly convex function and gives the proof of linear convergence rate. 2. A modified conjugate gradient formula MLS k β based on the formula of the Liu -Storey (LS) nonlinear conjugate gradient method is proposed. It

9、 is proved that under the Wolfe-Powell line search and even under the strong Wolfe-Powell line search ,meanwhile the parameter 1 (0, ) 2 σ ∈ , the corresponding method has sufficient descent and global convergence proper

10、ties. Numerical results show that the proposed method is very promising. 3. We proposed a spectral conjugate gradient method by combining conjugate gradient method and spectral gradient methodIn, the direction generated

11、by the method is a descent direction for the objective function, and this property depends neither on the line search rule, nor on the convexity of the objective function. Moreover, the modified method reduces to the sta