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

Author

Listed:
  • Saeed Ketabchi

    (University of Guilan)

  • Hossein Moosaei

    (University of Guilan)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:3:d:10.1007_s10957-012-0044-3
    DOI: 10.1007/s10957-012-0044-3
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    References listed on IDEAS

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    1. C. Kanzow & H. Qi & L. Qi, 2003. "On the Minimum Norm Solution of Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 116(2), pages 333-345, February.
    2. O. L. Mangasarian, 2004. "A Newton Method for Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 1-18, April.
    3. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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    Cited by:

    1. Xu Zhang & Cailian Li & Longcheng Zhang & Yaling Hu & Zheng Peng, 2024. "Convergence-Accelerated Fixed-Time Dynamical Methods for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 600-628, October.
    2. Yuan Liang & Chaoqian Li, 2023. "Modified Picard-like Method for Solving Absolute Value Equations," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    3. Saeed Ketabchi & Hossein Moosaei & Mohamad Razzaghi & Panos M. Pardalos, 2019. "An improvement on parametric $$\nu $$ ν -support vector algorithm for classification," Annals of Operations Research, Springer, vol. 276(1), pages 155-168, May.
    4. 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.

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