Viscous Approximations of Non-Convex Sweeping Processes in the Space of Regulated Functions

Vanishing viscosity approximations are considered here for discontinuous sweeping processes with non-convex constraints. It is shown that they are well-posed for sufficiently small viscosity parameters, and that their solutions converge pointwise, as the viscosity parameter tends to zero, to the lef...

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Veröffentlicht in:	Set-valued and variational analysis 2023-12, Vol.31 (4), Article 34
Hauptverfasser:	Krejčí, Pavel, Monteiro, Giselle A., Recupero, Vincenzo
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Sprache:	eng
Schlagworte:	Analysis Approximation Convergence Mathematics Mathematics and Statistics Optimization Parameters Sweeping Viscosity
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description	Vanishing viscosity approximations are considered here for discontinuous sweeping processes with non-convex constraints. It is shown that they are well-posed for sufficiently small viscosity parameters, and that their solutions converge pointwise, as the viscosity parameter tends to zero, to the left-continuous solution to the sweeping process in the Kurzweil integral setting. The convergence is uniform if the input is continuous.
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title	Viscous Approximations of Non-Convex Sweeping Processes in the Space of Regulated Functions
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