Abstract
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.
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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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This research has been partially supported by Grant MTM2014-59179-C2-2-P from MINECO, Spain, and FEDER “Una manera de hacer Europa”, European Union, and by the Vietnam National University - Ho Chi Minh city, Vietnam, Project Gerneralized scalar and vector Farkas-type results with applications to optimization theory.
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Cánovas, M.J., Dinh, N., Long, D.H. et al. An approach to calmness of linear inequality systems from Farkas lemma. Optim Lett 13, 295–307 (2019). https://doi.org/10.1007/s11590-018-01380-y
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DOI: https://doi.org/10.1007/s11590-018-01380-y