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

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  • De Wolf, Daniel
  • Smeers, Yves

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

  • 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.
    • Handle: RePEc:eee:ejores:v:291:y:2021:i:2:p:491-496
    DOI: 10.1016/j.ejor.2019.11.020
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    References listed on IDEAS

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    1. 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.
    2. 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).
    3. 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.
    4. 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.
    5. 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).
    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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