解非线性约束方程的拉格朗日全局投影方法  

Lagrangian Globalization Projection Methods for Nonlinear Constrained Equations

作　　者：童小娇[1] 何伟[1] 

机构地区：[1]长沙理工大学数学与计算科学学院,长沙410077

出　　处：《数学物理学报（A辑）》2008年第1期96-108,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(60474070);湖南省科技项目(06FJ3038);湖南省教育厅(07A001)资助

摘　　要：基于最优化方法求解约束非线性方程组的一个突出困难是计算得到的仅是该优化问题的稳定点或局部极小点,而非方程组的解点.由此引出的问题是如何从一个稳定点出发得到一个相对于方程组解更好的点.该文采用投影型算法,推广了Nazareth-Qi求解无约束非线性方程组的拉格朗日全局算法(Lagrangian Global-LG)于约束方程上;理论上证明了从优化问题的稳定点出发,投影LG方法可寻找到一个更好的点.数值试验证明了LG方法的有效性.To solve constrained nonlinear equations based on optimization algorithms is suffered a difficulty that the authors obtain just a stationary point or a local minimizer of the underlying optimization problem, which is not necessarily a solution of the equations. Then the arising problem is how to get a better point from the stationary point or the local minimizer point. By using a projection-type method, this paper extends the Lagrangian globalization （LG） method^ [8, 9] to a system of nonlinear equations with bounded constraints. The authors prove that from a stationary point, the LG projection method can find a better point. Numerical examples also show that the LG method has a potential to escape the stationary point of optimization problems.

关 键 词：约束方程组 拉格朗日全局算法 稳定点 全局收敛. 

分 类 号：O221.2[理学—运筹学与控制论]