Apart Sets and Functions: an Application to the Stability of Penalized Optimization Problems
Résumé
The notion of apart sets and functions, a technical concept introduced by Luc and Penot, is studied in the framework of star-shaped sets and functions. As an application, we provide a necessary and sufficient condition ensuring that a penalized optimization problem is stable with respect to perturbations of both the penalty and the objective functions, in the case when the perturbations are small in the sense of the Attouch-Wets topology.