Lipschitz lower semicontinuity moduli for linear inequality systems Articles uri icon

publication date

  • October 2020

start page

  • 1

end page

  • 21

issue

  • 2

volume

  • 490

International Standard Serial Number (ISSN)

  • 0022-247X

Electronic International Standard Serial Number (EISSN)

  • 1096-0813

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.

keywords

  • variational analysis; lipschitz lower semicontinuity; lipschitz modulus; aubin property; feasible set mapping; linear programming