M. J. Gisbert Francés, M. J. Cánovas Cánovas, R. Henrion, J. Parra López
In this talk we focus on the Lipschitz lower semicontinuity (Lipschitz-lsc, in brief) of the feasible set mapping for linear (finite and semi-infinite) inequality systems. This property measures the rate of local contraction (in a neighborhood of a given nominal solution) of the feasible set under data perturbations. At the same time we introduce the intermediate property between Aubin’s and Lipschitz lower semicontinuity, which we call Lipschitz lower semicontinuity* (Lipschitz-lsc*, in brief) inspired by previous works of D. Klatte (1985, 1987). Specifically, we study the relevancy of this property and its relationship between the others through their moduli. As we show, all these properties (Lipschitz-lsc, Lipschitz-lsc*, and Aubin) are equivalent when we deal with full or right-hand-side perturbations (the corresponding moduli do coincide). However, when we analyze the case of left-hand-side perturbations the situation is notably different.
Palabras clave: Lipschitz lower semicontinuity, feasible set mapping, linear programming, Aubin property, Lipschitz modulus, variational analysis
Programado
GT11-2 MA-2 Optimización Continua. Homenaje a Marco Antonio López
5 de septiembre de 2019 16:05
I2L7. Edificio Georgina Blanes