摘要
绝对值方程是一类NP难的方程,其一般形式为Ax-|x|=b,其中A∈R^(n×n),b∈R^n.通过把绝对值方程转化为等价的无约束优化问题,给出了求解此类绝对值方程的光滑化梯度法,并且给出了算法的全局性收敛性质.最后的数值实验证明了算法的实际有效性.
The absolute value equations are one of the NP-hard equations where Ax-｜x｜=b and A∈R^（n×n） is an arbitrary n×n real matrix,b∈R^n.By utilizing an equivalence relation,the equations are transformed to the unconstrained optimization problem,a smoothing gradient method is proposed to solve this kind of absolute value equations.The global convergence of the smoothing gradient method is also analyzed.Finally,some computational results show that this smoothing gradient method is efficient in practice.
出处
《江苏师范大学学报（自然科学版）》
CAS
2016年第1期35-38,共4页
Journal of Jiangsu Normal University：Natural Science Edition
基金
Research supported by the National Natural Science Foundation of China(11101231,11401331)
Natural Science Foundation of Shandong Province(ZR2015AQ013)
Key Issues of Statistical Research in Shandong Province(KT15173)
关键词
绝对值方程
光滑化梯度法
全局收敛
absolute value equation
smoothing gradient method
global convergence
