Article Dans Une Revue Set-Valued and Variational Analysis Année : 2025

Penalization and Necessary Optimality Conditions for a Class of Nonsmooth Sweeping Processes

Résumé

Abstract In this paper we derive necessary optimality conditions for a Mayer problem involving a controlled sweeping process characterized by a moving set which is merely locally prox-regular (not necessarily smooth) and satisfies a constraint qualification condition formulated exclusively in terms of its normal vectors. We employ a penalization method based on the distance from the moving constraint, which allows convergence estimates that are uniform with respect to the control and, moreover, the strong $W^{1,2}$ W 1 , 2 -convergence of the approximating solutions. An example of nonsmooth mechanics with finite degrees of freedom is presented.

Dates et versions

hal-05238759 , version 1 (03-09-2025)

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Piernicola Bettiol, Giovanni Colombo, Paolo Gidoni. Penalization and Necessary Optimality Conditions for a Class of Nonsmooth Sweeping Processes. Set-Valued and Variational Analysis, 2025, 33 (3), pp.33. ⟨10.1007/s11228-025-00770-6⟩. ⟨hal-05238759⟩
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