Optimization Letters

, Volume 13, Issue 2, pp 295–307 | Cite as

An approach to calmness of linear inequality systems from Farkas lemma

  • M. J. Cánovas
  • N. Dinh
  • D. H. Long
  • J. ParraEmail author
Original Paper


We deal with the feasible set mapping of linear inequality systems under right-hand side perturbations. From a version of Farkas lemma for difference of convex functions, we derive an operative relationship between calmness constants for this mapping at a nominal solution and associated neighborhoods where such constants work. We also provide illustrative examples where this approach allows us to compute the sharp Hoffman constant at the nominal system.


Calmness Hoffman constants Local error bounds Global error bounds Feasible set mapping Linear programming Variational analysis 



The authors wish to thank the anonymous referees for their deep review of the original manuscript, which has definitely improved the quality of the paper.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Center of Operations ResearchMiguel Hernández University of ElcheElcheSpain
  2. 2.Department of MathematicsInternational University Vietnam National University-Ho Chi Minh CityHo Chi Minh CityVietnam
  3. 3.VNUHCM - University of ScienceHo Chi Minh cityVietnam
  4. 4.Tien Giang UniversityTien Giang townVietnam

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