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

Authors :
Yves Smeers
Daniel De Wolf
Territoires, Villes, Environnement & Société - ULR 4477 (TVES)
Université du Littoral Côte d'Opale (ULCO)-Université de Lille
Université du Littoral Côte d'Opale (ULCO)
Université Catholique de Louvain = Catholic University of Louvain (UCL)
Center of Operation Research and Econometrics [Louvain] (CORE)
UCL - SSH/LIDAM/CORE - Center for operations research and econometrics
Université Catholique de Louvain (UCL)
Source :
European Journal of Operational Research, European Journal of Operational Research, Elsevier, 2019, European Journal of Operational Research, 291 (2), pp.Pages 491-496. ⟨10.1016/j.ejor.2019.11.020⟩, European Journal of Operational Research, Vol. 2, no. 291, p. 491-496 (2021), European Journal of Operational Research, Elsevier, 2021, 291, pp.491-496. ⟨10.1016/j.ejor.2019.11.020⟩, European Journal of Operational Research, (2019), European Journal of Operational Research, 2021, 291 (2), pp.491-496. ⟨10.1016/j.ejor.2019.11.020⟩, European Journal of Operational Research, 2019, 291 (2), pp.491-496. ⟨10.1016/j.ejor.2019.11.020⟩, European Journal of Operational Research, Elsevier, 2019, ⟨10.1016/j.ejor.2019.11.020⟩
Publication Year :
2019
Publisher :
HAL CCSD, 2019.

Abstract

International audience; 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.

Details

Language :
English
ISSN :
03772217 and 18726860
Database :
OpenAIRE
Journal :
European Journal of Operational Research, European Journal of Operational Research, Elsevier, 2019, European Journal of Operational Research, 291 (2), pp.Pages 491-496. ⟨10.1016/j.ejor.2019.11.020⟩, European Journal of Operational Research, Vol. 2, no. 291, p. 491-496 (2021), European Journal of Operational Research, Elsevier, 2021, 291, pp.491-496. ⟨10.1016/j.ejor.2019.11.020⟩, European Journal of Operational Research, (2019), European Journal of Operational Research, 2021, 291 (2), pp.491-496. ⟨10.1016/j.ejor.2019.11.020⟩, European Journal of Operational Research, 2019, 291 (2), pp.491-496. ⟨10.1016/j.ejor.2019.11.020⟩, European Journal of Operational Research, Elsevier, 2019, ⟨10.1016/j.ejor.2019.11.020⟩
Accession number :
edsair.doi.dedup.....172157c0e6a0332e324fae7f873b3488
Full Text :
https://doi.org/10.1016/j.ejor.2019.11.020⟩