求解非线性系统的信赖域方法  

A Trust Region Method for Nonlinear System

作　　者：王希云[1] 仝建[1] 

机构地区：[1]太原科技大学应用科学学院,山西030024

出　　处：《工程数学学报》2008年第1期133-137,共5页Chinese Journal of Engineering Mathematics

基　　金：山西省高校科技开发项目(200455)

摘　　要：本文给出了一个求解非线性系统的信赖域方法。通过引入松驰变量将非线性系统问题转化为带非负约束的非线性最优化问题,新算法借助于KKT条件和F-BNCP函数,在每次迭代时,不必求解二次信赖域子问题,只需求解一个线性方程组。在一定的假设条件下,该算法还是全局收敛和局部超线性收敛的。数值试验结果表明该算法是有效的。This paper presents a trust region method for nonlinear system. This problem is first transformed into a nonlinear optimization with nonnegative constraints by introducing slack variables. Then, without solving a quadratic trust region sub-problem, a system of linear equations is solved to find a search direction with the aid of to the KKT condition and F-B the NCP function. Under certain conditions, this algorithm is globally convergent and locally super-linear convergent. Numerical experiments show that the algorithm is effective.

关 键 词：非线性系统 信赖域方法 KKT点 F-B NCP函数 

分 类 号：O221.1[理学—运筹学与控制论]