Explicit and implicit non-convex sweeping processes in the space of\n absolutely continuous functions

2020/05/21 by Pavel Krejčı́, Krejci, Pavel, Giselle Antunes Monteiro +3 · 1 citation
Computer Science · Mathematics · #34A60 #34G25 #47J20 #49J52 #74C05 #Advanced Banach Space Theory #Advanced Optimization Algorithms Research #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2005.10942

openalex publication_date 2020/05/21 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We show that sweeping processes with possibly non-convex prox-regular\nconstraints generate a strongly continuous input-output mapping in the space of\nabsolutely continuous functions. Under additional smoothness assumptions on the\nconstraint we prove the local Lipschitz continuity of the input-output mapping.\nUsing the Banach contraction principle, we subsequently prove that also the\nsolution mapping associated with the state-dependent problem is locally\nLipschitz continuous.\n

Cited by

• Excess-continuous prox-regular sweeping processes

Related

• State-Dependent Sweeping Processes: Asymptotic Behavior and Algorithmic Approaches
• Non-convex sweeping processes in the space of regulated functions
• Prox-regular sweeping processes with bounded retraction
• Convex valued geodesics and applications to sweeping processes with bounded retraction
• Solution Properties of Convex Sweeping Processes with Velocity\n Constraint