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

Iranian Journal of Numerical Analysis and Optimization

مقاله 3، دوره 7، شماره 2 - شماره پیاپی 12، دی 2017، صفحه 57-64   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v7i2.57912

نویسندگان

S. Ketabchi¹؛ H. Moosaei^{* 2}

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

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

چکیده

‎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.

کلیدواژه‌ها

Absolute value equation؛ Minimum norm solution؛ Generalized Newton method؛ Augmented Lagrangian method

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