TY - JOUR
T1 - A Smoothing Technique for the Minimum Norm Solution of Absolute Value Equation
TT - یک روش هموارسازی برای محاسبه جواب با کمترین نرم دستگاه معادلات قدرمطلق
JF - JAMLU
JO - JAMLU
VL - 16
IS - 1
UR - http://jamlu.liau.ac.ir/article-1-1608-en.html
Y1 - 2019
SP - 1
EP - 9
KW - Absolute Value Equation
KW - Augmented Lagrangian Method
KW - Minimum Norm Solution
KW - Smoothing Techniques
N2 - One of the issues that has been considered by the researchers in terms of theory and practice is the problem of finding minimum norm solution. In fact, in general, absolute value equation may have inﬁnitely many solutions. In such cases, the best and most natural choice is the solution with the minimum norm. In this paper, the minimum norm-1 solution of absolute value equation is investigated. By applying the augmented Lagrangian method, this problem can be reduced to an unconstrained optimization problem with once differentiable objective function. To use Newton method, we apply the smoothing techniques. Computational results show that convergence to high accuracy often occurs in just a few iterations.
M3
ER -