Citation:
Cánovas, M., Gisbert, M., Henrion, R. & Parra, J. (2020). Lipschitz lower semicontinuity moduli for linear inequality systems. Journal of Mathematical Analysis and Applications, 490(2), 124313.
xmlui.dri2xhtml.METS-1.0.item-contributor-funder:
Ministerio de Economía y Competitividad (España)
Sponsor:
This research has been partially supported by Grants MTM2014-59179-C2-2-P and PGC2018-097960-B-C21 from MINECO/MICINN, Spain and ERDF, "A way to make Europe", European Union.
Project:
Gobierno de España. MTM2014-59179-C2-2-P Gobierno de España. PGC2018-097960-B-C21
Keywords:
Variational analysis
,
Lipschitz lower semicontinuity
,
Lipschitz modulus
,
Aubin property
,
Feasible set mapping
,
Linear programming
The paper is focussed on the Lipschitz lower semicontinuity of the feasible set mapping for linear (finite and infinite) inequality systems in three different perturbation frameworks: full, right-hand side and left-hand side perturbations. Inspired by [14], weThe paper is focussed on the Lipschitz lower semicontinuity of the feasible set mapping for linear (finite and infinite) inequality systems in three different perturbation frameworks: full, right-hand side and left-hand side perturbations. Inspired by [14], we introduce the Lipschitz lower semicontinuity-star as an intermediate notion between the Lipschitz lower semicontinuity and the well-known Aubin property. We provide explicit point-based formulae for the moduli (best constants) of all three Lipschitz properties in all three perturbation settings.[+][-]