Filters

2015 - 20192

More filters

2019 - 201912020 - 20221
Reset filters

Settings

Subject: Variational analysis ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Lipschitz lower semicontinuity moduli for linear inequality systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Cánovas, Maria Josefa; Gisbert, María Jesús; Henrion, René; Parra, Juan
    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.
  • Thumbnail Image
    Item
    Critical objective size and calmness modulus in linear programming
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Cánovas, Maria J.; Henrion, René; Parra, Juan; Toledo, F. Javier
    This paper introduces the concept of critical objective size associated with a linear program in order to provide operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating the calmness modulus of the optimal set (argmin) mapping under uniqueness of nominal optimal solution and perturbations of all coefficients. Our starting point is an upper bound on this modulus given in [4]. In this paper we prove that this upper bound is attained if and only if the norm of the objective function coefficient vector is less than or equal to the critical objective size. This concept also allows us to obtain operative lower bounds on the calmness modulus. We analyze in detail an illustrative example in order to xplore some strategies that can improve the referred upper and lower bounds.