有界约束非线性方程组的仿射共轭梯度路径法  

AN AFFINE SCALING CONJUGATE GRADIENT PATH METHOD FOR BOUND-CONSTRAINED NONLINEAR EQUALITY SYSTEMS

作　　者：张勇[1] 朱德通[2] 

机构地区：[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

出　　处：《高等学校计算数学学报》2011年第1期67-80,共14页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金项目(编号10871130);博士点基金项目(编号20093127110005);上海市重点学科项目(编号T0401)

摘　　要：1引言本文研究约束非线性方程组的问题F(x)=0,x∈Ω.(1.1)In this paper, we propose an approach of afflne scaling interior discrete conjugate gradient path for solving nonlinear equality systems subject to bounds on variable. By constructing preconditioned discrete conjugate gradient path, we obtain an iterative search direction. By combining interior backtracking line search, we find an acceptable trial step length. The search direction and step length which are obtained possess good properties. The global convergence and local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the numerical results indicate the effectiveness of the algorithm.

关 键 词：有界约束非线性方程组 仿射共轭梯度路径法 解法 数学 

分 类 号：O17[理学—数学]