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Tikhonov regularization for infeasible absolute value equations |
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| Authors: | Hossein Moosaei Saeed Ketabchi Panos M Pardalos |
| Institution: | 1. Faculty of Science, Department of Mathematics, University of Bojnord, Bojnord, Iran.hmoosaei@gmail.commoosaei@ub.ac.ir;4. Faculty of Mathematical Sciences, Department of Applied Mathematics, University of Guilan, Rasht, Iran.;5. Department of Industrial and Systems Engineering, Center for Applied Optimization, University of Florida, Gainesville, Florida, USA. |
| Abstract: | We investigate the optimum correction of an absolute value equation by minimally changing the coefficient matrix and right-hand side vector using Tikhonov regularization. Solving this problem is equivalent to minimizing the sum of fractional quadratic and quadratic functions. The primary difficulty with this problem is its nonconvexity. Nonetheless, we show that a global optimal solution to this problem can be found by solving an equation on a closed interval using the subgradient method. Some examples are provided to illustrate the efficiency and validity of the proposed method. |
| Keywords: | Absolute value equation fractional programming optimal correction subgradients Tikhonov regularization |