Work

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

Year: 2025

Type: article

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.

Source: Set-Valued and Variational Analysis

DOI: 10.1007/s11228-025-00770-6

Authors: Piernicola Bettiol, Giovanni Colombo, Paolo Gidoni

Institutions: Centre National de la Recherche Scientifique, Université de Bretagne Occidentale, Laboratoire de Mathématiques de Bretagne Atlantique, University of Padua, University of Udine

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Agence Nationale de la Recherche