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Optimal correction of the absolute value equations

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Abstract

In this paper, we study the optimum correction of the absolute value equations through making minimal changes in the coefficient matrix and the right hand side vector and using spectral norm. This problem can be formulated as a non-differentiable, non-convex and unconstrained fractional quadratic programming problem. The regularized least squares is applied for stabilizing the solution of the fractional problem. The regularized problem is reduced to a unimodal single variable minimization problem and to solve it a bisection algorithm is proposed. The main difficulty of the algorithm is a complicated constraint optimization problem, for which two novel methods are suggested. We also present optimality conditions and bounds for the norm of the optimal solutions. Numerical experiments are given to demonstrate the effectiveness of suggested methods.

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Acknowledgements

The work of H. Moosaei and M. Hladík was supported by the Czech Science Foundation Grant P403-18-04735S.

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Authors and Affiliations

  1. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Prague, Czech Republic

    Hossein Moosaei & Milan Hladík

  2. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

    Saeed Ketabchi

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

    Hossein Moosaei

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  1. Hossein Moosaei
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  2. Saeed Ketabchi
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  3. Milan Hladík
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Correspondence to Milan Hladík.

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Moosaei, H., Ketabchi, S. & Hladík, M. Optimal correction of the absolute value equations. J Glob Optim 79, 645–667 (2021). https://doi.org/10.1007/s10898-020-00948-2

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