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

Daniel de Wolf () and Yves Smeers
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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

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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.

Keywords: Non- differentiable programming; Linear programming; Parametric linear programming (search for similar items in EconPapers)
Date: 2021-06-01
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-02396708v2
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Citations: View citations in EconPapers (1)

Published in European Journal of Operational Research, 2021, 291 (2), pp.491-496. ⟨10.1016/j.ejor.2019.11.020⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-02396708

DOI: 10.1016/j.ejor.2019.11.020

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