Explicit and Implicit Non-convex Sweeping Processes in the Space of Absolutely Continuous Functions
We show that sweeping processes with possibly non-convex prox-regular constraints generate a strongly continuous input-output mapping in the space of absolutely continuous functions. Under additional smoothness assumptions on the constraint we prove the local Lipschitz continuity of the input-output...
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| Veröffentlicht in: | Applied mathematics & optimization 2021-12, Vol.84 (Suppl 2), p.1477-1504 |
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| container_title | Applied mathematics & optimization |
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| creator | Krejčí, Pavel Monteiro, Giselle Antunes Recupero, Vincenzo |
| description | We show that sweeping processes with possibly non-convex prox-regular constraints generate a strongly continuous input-output mapping in the space of absolutely continuous functions. Under additional smoothness assumptions on the constraint we prove the local Lipschitz continuity of the input-output mapping. Using the Banach contraction principle, we subsequently prove that also the solution mapping associated with the state-dependent problem is locally Lipschitz continuous. |
| doi_str_mv | 10.1007/s00245-021-09801-8 |
| format | Article |
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| subjects | Applied mathematics Calculus of Variations and Optimal Control Optimization Continuity (mathematics) Control Hilbert space Hypotheses Mapping Mathematical and Computational Physics Mathematical functions Mathematical Methods in Physics Mathematics Mathematics and Statistics Numerical and Computational Physics Optimization Original Paper Simulation Smoothness Sweeping Systems Theory Theoretical |
| title | Explicit and Implicit Non-convex Sweeping Processes in the Space of Absolutely Continuous Functions |
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