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Generalized Derivatives of Lexicographic Linear Programs

Author

Listed:
  • Jose Alberto Gomez

    (Massachusetts Institute of Technology)

  • Kai Höffner

    (Massachusetts Institute of Technology)

  • Kamil A. Khan

    (Massachusetts Institute of Technology
    McMaster University)

  • Paul I. Barton

    (Massachusetts Institute of Technology)

Abstract

Lexicographic linear programs are fixed-priority multiobjective linear programs that are a useful model of biological systems using flux balance analysis and for goal-programming problems. The objective function values of a lexicographic linear program as a function of its right-hand side are nonsmooth. This work derives generalized derivative information for lexicographic linear programs using lexicographic directional derivatives to obtain elements of the Bouligand subdifferential (limiting Jacobian). It is shown that elements of the limiting Jacobian can be obtained by solving related linear programs. A nonsmooth equation-solving problem is solved to illustrate the benefits of using elements of the limiting Jacobian of lexicographic linear programs.

Suggested Citation

  • Jose Alberto Gomez & Kai Höffner & Kamil A. Khan & Paul I. Barton, 2018. "Generalized Derivatives of Lexicographic Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 477-501, August.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:2:d:10.1007_s10957-018-1309-2
    DOI: 10.1007/s10957-018-1309-2
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    References listed on IDEAS

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    1. NESTEROV, Yu., 2005. "Lexicographic differentiation of nonsmooth functions," LIDAM Reprints CORE 1817, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Kamil A. Khan & Paul I. Barton, 2014. "Generalized Derivatives for Solutions of Parametric Ordinary Differential Equations with Non-differentiable Right-Hand Sides," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 355-386, November.
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    Cited by:

    1. De Wolf, Daniel & Smeers, Yves, 2021. "Generalized derivatives of the optimal value of a linear program with respect to matrix coefficients," European Journal of Operational Research, Elsevier, vol. 291(2), pages 491-496.
    2. Daniel de Wolf & Yves Smeers, 2021. "Generalized derivatives of the optimal value of a linear program with respect to matrix coefficients," Post-Print halshs-02396708, HAL.

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