Minimum Norm Solution to the Absolute Value Equation in the Convex Case

Saeed Ketabchi () and Hossein Moosaei ()
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Saeed Ketabchi: University of Guilan
Hossein Moosaei: University of Guilan

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 3, No 19, 1080-1087

Abstract: Abstract In this paper, we give an algorithm to compute the minimum norm solution to the absolute value equation (AVE) in a special case. We show that this solution can be obtained from theorems of the alternative and a useful characterization of solution sets of convex quadratic programs. By using an exterior penalty method, this problem can be reduced to an unconstrained minimization problem with once differentiable convex objective function. Also, 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; Solution sets of convex programs (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-012-0044-3

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