M. J. Cánovas Cánovas, J. Parra López
This talk is concerned with the Aubin property of the feasible and optimal set mappings in convex optimization in different parametric settings. Specifically, regarding convex inequalities, we deal with right-hand side (RHS), affine, and free perturbations of the original data, while convex programs are canonically perturbed (i.e., the objective function is linearly perturbed and the constraint system is subject to RHS perturbations). Together with a survey of results on the Aubin property and its associated Lispchitz modulus, our focus is on the technics followed to derive them. In particular, a supremum function approach and a linearization strategy based on the Fenchel-Legendre conjugate are discussed. Combining both strategies and appealing to a recent Ascoli-type result on the distance from a point to the solution set of a convex inequality, we derive a new proof of previous results.
Palabras clave: Stability, Lipschitz modulus, convex optimization, parametric optimization
Programado
Métodos y aplicaciones de la IO III
13 de junio de 2025 11:00
Sala de prensa (MR 13)