解非线性最小二乘问题的锥模型算法  

CONIC MODEL ALGORITHMS FOR NONLINEAR LEAST-SQUARES PROBLEMS

作　　者：韩乔明[1] 盛松柏[1] 

机构地区：[1]南京大学数学系,210093

出　　处：《高等学校计算数学学报》1995年第1期48-59,共12页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家及江苏省自然科学基金

摘　　要：在自然科学研究、经济、统计等领域,非线性最小二乘有着广泛的应用,因而寻找快捷有效的算法有着十分重要的意义。它首先是一个最优化问题,同时又有自身的结构特点,充分利用其结构特点,是寻找更有效算法的关键。In this paper,we develope and test a new algorithm for nonlinear least squares problems. The algorithm uses a DFP analogue update of the Gauss-Newton Hessian with a conic model. Some important elements are that the secant or quasi-Newton equations considered are not the obvious ones, and the method needs to solve a trust region problem with an objective function of conic model. The algorithm can be implemented easily as a modification of any trust region method, and it seems to be useful for ill condition problems.

关 键 词：最小二乘问题 锥模型 算法 非线性 最佳化 

分 类 号：O224[理学—运筹学与控制论]