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Generalized derivatives of the optimal value of a linear program with respect to matrix coefficients

Author

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  • Daniel de Wolf

    (TVES - Territoires, Villes, Environnement & Société - ULR 4477 - ULCO - Université du Littoral Côte d'Opale - Université de Lille, CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain = Catholic University of Louvain, ULCO - Université du Littoral Côte d'Opale)

  • Yves Smeers

    (UCL - Université Catholique de Louvain = Catholic University of Louvain, CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain = Catholic University of Louvain)

Abstract

We present here a characterization of the Clarke subdifferential of the optimal value function of a linear program as a function of matrix coefficients. We generalize the result of Freund (1985) to the cases where derivatives may not be defined because of the existence of multiple primal or dual solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:hal:journl:halshs-02396708
    DOI: 10.1016/j.ejor.2019.11.020
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-02396708v2
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    References listed on IDEAS

    as
    1. De Wolf, D. & Smeers, Y., 1996. "Optimal dimensioning of pipe networks with application to gas transmission networks," LIDAM Reprints CORE 1249, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Jacques Gauvin, 1979. "The Generalized Gradient of a Marginal Function in Mathematical Programming," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 458-463, November.
    3. 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.
    4. DE WOLF, Daniel & SMEERS, Yves, 2000. "The gas transmission problem solved by an extension of the simplex algorithm," LIDAM Reprints CORE 1489, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Daniel de Wolf & Yves Smeers, 1996. "Optimal Dimensioning of Pipe Networks with Application to Gas Transmission Networks," Operations Research, INFORMS, vol. 44(4), pages 596-608, August.
    6. Daniel De Wolf & Yves Smeers, 2000. "The Gas Transmission Problem Solved by an Extension of the Simplex Algorithm," Management Science, INFORMS, vol. 46(11), pages 1454-1465, November.
    Full references (including those not matched with items on IDEAS)

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