Lipschitz modulus of linear and convex systems with the Hausdorff metric

M. J. Cánovas Cánovas, G. Beer, M. A. López Cerdá, J. Parra López

This talk is focussed on the Lipschitz behavior of the feasible set in two parametric settings, associated with linear and convex systems in the finite dimensional Euclidean space. To start with, we deal with the parameter space of linear (finite/semi-infinite) systems identified with the corresponding sets of coefficient vectors, and the Hausdorff distance is used to measure the size of perturbations. In this setting, an explicit formula for the Lipschitz modulus of the feasible set mapping is provided. As direct antecedent, we appeal to its counterpart in the parameter space of all linear systems with a fixed index set, where the Chebyshev (pseudo) distance was considered. Here, through an appropriate indexation strategy, we take advantage of the background to derive the new results in the Hausdorff setting. In a second stage, the talk presents new contributions on the Lipschitz behavior of convex systems via linearization techniques.

Keywords: Lipschitz modulus, feasible set mapping, Hausdorff metric, indexation

GT11-6 MA-6 Continuous Optimization. Tribute to Marco Antonio López
September 6, 2019  3:30 PM
I2L7. Georgina Blanes building

M. A. López Cerdá, G. Beer, M. J. Cánovas Cánovas, J. Parra López

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