Camacho, J., Cánovas, M.J., Parra, J. (2022) “Lipschitz upper semicontinuity in linear optimization via local directional convexity”, Optimization,

Jesús Camacho, María Josefa Cánovas and Juan Parra (Operations Research Center, University Miguel Hernández of Elche) 

Abstract: This work is focussed on computing the Lipschitz upper semicontinuity modulus of the argmin mapping for canonically perturbed linear programs. The immediate antecedent can be traced out from Camacho J et al. [2022. From calmness to Hoffman constants for linear semi-infinite inequality systems. Available from: https://arxiv.org/pdf/2107.10000v2.pdf], devoted to the feasible set mapping. The aimed modulus is expressed in terms of a finite amount of calmness moduli, previously studied in the literature. Despite the parallelism in the results, the methodology followed in the current paper differs notably from Camacho J et al. [2022] as far as the graph of the argmin mapping is not convex; specifically, a new technique based on a certain type of local directional convexity is developed.