不等式约束非线性最小二乘问题的一个解法  

A method for inequality constrained nonlinear least squares problems

作　　者：徐成贤[1] 

机构地区：[1]西安交通大学

出　　处：《工程数学学报》1989年第1期33-39,共7页Chinese Journal of Engineering Mathematics

摘　　要：1 引言 不等式约束非线性最小二乘问题 属非线性规划问题,其中r_i,c_j一般为非线性的连续函数。设F,c_j二阶连续可导且问题(1.1)有最优解,记为x~*。用S~*={j:c_j(x~*)=0,1≤j≤p}表示在点x~*处的有效约束集合,并设在x~*处、下列最优解的一阶必要与二阶充分条件满足:(ⅰ)Δc_j~*,j∈S~*线性无关;(ⅱ)存在Lagrange乘子λ~*∈R^pThis paper presents a method for solving inequality constrained nonlinear least squares problems. Multiplier penalty function is employed to transfer the problem into the solution of a series of unconstrained nonlinear least squar.es problems which are solved using the hybrid GN-BFGS method (Fletcher & Xu, 1987).Successive minimization is inexact and modifications to Powell (1969) and Fletcher's (1975) formulae for adjusting the parameter vector are suggested. Numerical results are given to show the efficiency of the suggested method.

关 键 词：非线性规划 GN-BFGS方法 

分 类 号：TB114.1[理学—运筹学与控制论]