基于凝聚函数的拟牛顿算法求解绝对值方程  

QUASI-NEWTON METHOD TO ABSOLUTE VALUE EQUATIONS BASED ON AGGREGATE FUNCTION

作　　者：雍龙泉[1] 拓守恒[1] 

机构地区：[1]陕西理工学院数学与计算机科学学院,汉中723001

出　　处：《系统科学与数学》2012年第11期1427-1436,共10页Journal of Systems Science and Mathematical Sciences

基　　金：陕西省教育厅自然科学研究项目(12JK0863)

摘　　要：绝对值方程Ax-|x|=b是一个不可微的NP-hard问题.在假设矩阵A的奇异值大于1(这里矩阵A的奇异值定义为矩阵A^TA特征值的非负平方根)时,给出了求解绝对值方程一个新的光滑化算法.通过引入一种凝聚函数对绝对值方程进行光滑化处理,得到一个非线性方程组;再引入适当的目标函数,进而把绝对值方程化为无约束优化问题,然后利用拟牛顿算法对其进行求解.数值实验结果表明了该方法的正确性和有效性.Absolute value equations Ax- ｜x｜ = b is a nomdifferentiable NP-hard problem in its general form. In this paper, a new smoothing method for solving absolute value equations is proposed under the condition that all singular values of A exceed one. First, by using the aggregate function, absolute value equations is transformed into a smooth nonlinear equation, and then into an unconstrained differentiable optimization problem by introducing appropriate objective function. Finally, we apply quasi-Newton method to solve this problem. Numerical results indicate that the method is feasible and effective to absolute value equations.

关 键 词：绝对值方程 拟牛顿算法 凝聚函数 

分 类 号：O241.6[理学—计算数学]