求解约束插值和光顺问题的信赖域方法  

Constrained Interpolation and Smoothing Problems Solved by a Trust Region Algorithm

作　　者：覃廉[1] 关履泰[1] 谢骊玲[1] 

机构地区：[1]中山大学科学计算与计算机应用系,广东广州510275

出　　处：《中山大学学报（自然科学版）》2005年第B06期146-151,共6页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(60475042);广东省自然科学基金重点资助项目(036608);香港中山大学高等学术研究中心基金会资助

摘　　要：针对凸插值、凸光顺和保形插值等带约束条件的插值和光顺问题,提出一种信赖域方法。约束插值和光顺问题可归结为求解半光滑非线性方程组。本文利用半光滑方程组的广义雅可比矩阵,采用半光滑方程组的平方自然残余量作为价值函数。同时,利用关履泰(1983)关于凸集上样条函数的性质,改进信赖域方法,以加速信赖域方法的迭代。本文证明了求解约束插值和光顺问题的信赖域方法的局部收敛性和全局收敛性,最后给出了数值算例。This paper presents a trust region algorithm for solving the constrained interpolation and smoothing problems such as convex interpolation, convex smoothing and shape-preserving interpolation. All these problems can be reduced to semismooth nonlinear systems. Apply a generalized Jacobian of the function involved in semismooth equation and adopt the squared natural residual of the semismooth equation as a merit function. Furthermore,the trust region method is improved by the properties of the spline on a convex set, hence it can be speeded up the iteration of the trust region method.The local and global convergence of the trust region method in constrained interpolation and smoothing problems is shown.The end of the paper presents some numerical examples.

关 键 词：凸插值 凸光顺 保形插值 信赖域 半光滑方程组 外射集 

分 类 号：O24[理学—计算数学]