Camacho, J., Cánovas, M. J., & Parra, J. (2023). Lipschitz upper semicontinuity in linear optimization via local directional convexity. Optimization, 72(8), 2091–2108.

J.Camacho (Operations Research Center, University Miguel Hernández of Elche), M.J. Cánovas (Operations Research Center, University Miguel Hernández of Elche) and J.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.