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Optimal correction of the absolute value equations

Author

Listed:
  • Hossein Moosaei

    (Charles University
    Faculty of Science, University of Bojnord)

  • Saeed Ketabchi

    (University of Guilan)

  • Milan Hladík

    (Charles University)

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.

Suggested Citation

  • Hossein Moosaei & Saeed Ketabchi & Milan Hladík, 2021. "Optimal correction of the absolute value equations," Journal of Global Optimization, Springer, vol. 79(3), pages 645-667, March.
    • Handle: RePEc:spr:jglopt:v:79:y:2021:i:3:d:10.1007_s10898-020-00948-2
    DOI: 10.1007/s10898-020-00948-2
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    References listed on IDEAS

    as
    1. Oleg Prokopyev, 2009. "On equivalent reformulations for absolute value equations," Computational Optimization and Applications, Springer, vol. 44(3), pages 363-372, December.
    2. Saeed Ketabchi & Hossein Moosaei, 2012. "Optimal Error Correction and Methods of Feasible Directions," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 209-216, July.
    3. Moosaei, H. & Ketabchi, S. & Noor, M.A. & Iqbal, J. & Hooshyarbakhsh, V., 2015. "Some techniques for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 696-705.
    4. O. L. Mangasarian, 2004. "A Newton Method for Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 1-18, April.
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    6. Paula Amaral & Luís Fernandes & Joaquim Júdice & Hanif Sherali, 2009. "On optimal zero-preserving corrections for inconsistent linear systems," Computational Optimization and Applications, Springer, vol. 45(4), pages 645-666, December.
    7. Shi-Liang Wu & Peng Guo, 2016. "On the Unique Solvability of the Absolute Value Equation," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 705-712, May.
    8. Saeed Ketabchi & Hossein Moosaei, 2012. "Minimum Norm Solution to the Absolute Value Equation in the Convex Case," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 1080-1087, September.
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