@article { author = {Ketabchi, S. and Moosaei, H.}, title = {Augmented Lagrangian Method for Finding Minimum Norm Solution to the Absolute Value Equation}, journal = {Iranian Journal of Numerical Analysis and Optimization}, volume = {7}, number = {2}, pages = {57-64}, year = {2017}, publisher = {Ferdowsi University of Mashhad}, issn = {2423-6977}, eissn = {2423-6969}, doi = {10.22067/ijnao.v7i2.57912}, abstract = {‎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.}, keywords = {Absolute value equation,Minimum norm solution,Generalized Newton method,Augmented Lagrangian method}, url = {https://ijnao.um.ac.ir/article_24567.html}, eprint = {https://ijnao.um.ac.ir/article_24567_25c1b6aedf63ce96172f888d48396484.pdf} }