Augmented Lagrangian Method for Finding Minimum Norm Solution to the Absolute Value Equation

Document Type : Research Article


1 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran.

2 Department of Mathematics, Faculty of Science, University of Bojnord, Bojnord, Iran.


‎In 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.


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