Hoffman modulus of the argmin mapping in linear optimization

M. J. Cánovas Cánovas, J. Camacho Moro, H. Gfrerer, J. Parra López

In this talk we compute the global Hoffman constant of the optimal set (argmin) mapping for linear optimization problems under right-hand side (RHS) perturbations. Roughly speaking, we measure how the optimal set varies with respect to (nonnecessarily small) RHS perturbations. The global Hoffman constant turns out to be the maximum of calmness moduli at some outstanding points. When perturbations are taken with respect to a given parameter (RHS), we are dealing with the so-called Hoffman modulus at this parameter. We show that this quantity may be strictly less than the global Hoffman constant.

Keywords: Global Hoffman constant, Hoffman modulus, calmness modulus, argmin mapping, linear programming

GT13.OPTCONT3 Invited Session
November 7, 2023  3:30 PM
HC2: Canónigos Room 2

H. Gfrerer, J. Outrata

J. Rückmann, D. Hernández Escobar

J. Parra López, J. Camacho Moro, M. J. Cánovas Cánovas, J. E. Martínez Legaz