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

Daniel de Wolf (1, 2, 3) , Yves Smeers (4, 2)

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

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.

Mots clés: Non- differentiable programming; Linear programming; Parametric linear programming

Domaines: Gestion et management; Recherche opérationnelle [cs.RO]

Daniel de Wolf, Yves Smeers. Generalized derivatives of the optimal value of a linear program with respect to matrix coefficients. European Journal of Operational Research, 2021, 291 (2), pp.491-496. ⟨10.1016/j.ejor.2019.11.020⟩. ⟨halshs-02396708v2⟩