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On the Minimum Norm Solution of Linear Programs

Author

Listed:
  • C. Kanzow

    (University of Würzburg, Am Hubland)

  • H. Qi

    (Hong Kong Polytechnic University)

  • L. Qi

    (Hong Kong Polytechnic University)

Abstract

This paper describes a new technique to find the minimum norm solution of a linear program. The main idea is to reformulate this problem as an unconstrained minimization problem with a convex and smooth objective function. The minimization of this objective function can be carried out by a Newton-type method which is shown to be globally convergent. Furthermore, under certain assumptions, this Newton-type method converges in a finite number of iterations to the minimum norm solution of the underlying linear program.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:116:y:2003:i:2:d:10.1023_a:1022457904979
    DOI: 10.1023/A:1022457904979
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    References listed on IDEAS

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    1. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
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    Cited by:

    1. 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.
    2. 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.
    3. G. Zhou & K. C. Toh, 2005. "Superlinear Convergence of a Newton-Type Algorithm for Monotone Equations," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 205-221, April.
    4. Hossein Moosaei & Milan Hladík, 2021. "On the Optimal Correction of Infeasible Systems of Linear Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 32-55, July.
    5. M. J. Cánovas & M. J. Gisbert & D. Klatte & J. Parra, 2022. "Projection-Based Local and Global Lipschitz Moduli of the Optimal Value in Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 280-299, June.

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