An Existence Result for Discontinuous Second-Order Nonconvex State-Dependent Sweeping Processes

Samir Adly (1) , Florent Nacry (1)

1 XLIM-MATHIS - Mathématiques & Sécurité de l'information

In this paper, we study the existence of solutions for a time and state-dependent discontinuous nonconvex second order sweeping process with a multivalued perturbation. The moving set is assumed to be prox-regular, relatively ball-compact with a bounded variation. The perturbation of the normal cone is a scalarly upper semicontinuous convex valued multimapping satisfying a linear growth condition possibly time-dependent. As an application of the theoretical results, we investigate the theory of evolution quasi-variational inequalities.

Mots clés: Variational analysis; Measure differential inclusions; Second-order sweeping process; Prox-regular sets; Bounded variation; Variational inequalities

Domaines: Optimisation et contrôle [math.OC]

Samir Adly, Florent Nacry. An Existence Result for Discontinuous Second-Order Nonconvex State-Dependent Sweeping Processes. Applied Mathematics and Optimization, 2019, 79 (2), pp.515-546. ⟨10.1007/s00245-017-9446-9⟩. ⟨hal-02109884⟩