WIAS Preprint No. 2631, (2019)

Lipschitz lower semicontinuity moduli for linear inequality systems


  • Cánovas, Maria Josefa
  • Gisbert, María Jesús
  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Parra, Juan

2010 Mathematics Subject Classification

  • 90C31 49J53 49K40 90C05


  • 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], 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.

Appeared in

  • Discrete Contin. Dyn. Syst. Ser. S, 14 (2021), pp. 395--425 (published online in May 2020), DOI 10.3934/dcdss.2020345 .

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