Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69777220171001Augmented Lagrangian Method for Finding Minimum Norm Solution to the Absolute Value Equationروش ﻻﮔﺮاﻧﮋ ﺑﻬﺒﻮد ﯾﺎﻓﺘﻪ ﺑﺮای ﭘﯿﺪا ﮐﺮدن ﺟﻮاب ﺑﺎ ﮐﻤﺘﺮﯾﻦ ﻧﺮم- ١ دﺳﺘﮕﺎه ﻣﻌﺎدﻻت ﻗﺪر مطلق57642456710.22067/ijnao.v7i2.57912ENS.KetabchiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran.H.MoosaeiDepartment of Mathematics, Faculty of Science, University of Bojnord, Bojnord, Iran.Journal Article19700101In this paper, we give an algorithm to compute the minimum 1-norm solution to the absolute value equation (AVE). The augmented Lagrangian method is investigated for solving this problems . This approach leads to an unconstrained minimization problem with once differentiable convex objective function. We propose a quasi-Newton method for solving unconstrained optimization problem. Computational results show that convergence to high accuracy often occurs in just a few iterations.https://ijnao.um.ac.ir/article_24567_25c1b6aedf63ce96172f888d48396484.pdf