WIAS Preprint No. 2631, (2019)

Lipschitz lower semicontinuity moduli for linear inequality systems


Authors

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

2010 Mathematics Subject Classification

  • 90C31 49J53 49K40 90C05

Keywords

  • Variational analysis, Lipschitz lower semicontinuity, Lipschitz modulus, Aubin property, feasible set mapping, linear programming

DOI

10.20347/WIAS.PREPRINT.2631

Abstract

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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