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Projection-Based Local and Global Lipschitz Moduli of the Optimal Value in Linear Programming

Author

Listed:
  • M. J. Cánovas

    (Miguel Hernández University of Elche)

  • M. J. Gisbert

    (Universidad Carlos III de Madrid)

  • D. Klatte

    (Universität Zürich)

  • J. Parra

    (Miguel Hernández University of Elche)

Abstract

In this paper, we use a geometrical approach to sharpen a lower bound given in [5] for the Lipschitz modulus of the optimal value of (finite) linear programs under tilt perturbations of the objective function. The key geometrical idea comes from orthogonally projecting general balls on linear subspaces. Our new lower bound provides a computable expression for the exact modulus (as far as it only depends on the nominal data) in two important cases: when the feasible set has extreme points and when we deal with the Euclidean norm. In these two cases, we are able to compute or estimate the global Lipschitz modulus of the optimal value function in different perturbations frameworks.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:193:y:2022:i:1:d:10.1007_s10957-021-01948-2
    DOI: 10.1007/s10957-021-01948-2
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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.
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