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Lipschitz lower semicontinuity moduli for linear inequality systems

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URI: https://hdl.handle.net/10016/32996
ISSN: 0022-247X
DOI: https://doi.org/10.1016/j.jmaa.2020.124313
UXXI: AR/0000025767
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Lipschitz_JMAA_2020_ps.pdf (656 KB)
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2020-10-15
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Elsevier
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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], 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.
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Variational analysis, Lipschitz lower semicontinuity, Lipschitz modulus, Aubin property, Feasible set mapping, Linear programming
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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.
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