Moreau-Yosida Regularization of State-Dependent Sweeping Processes with Nonregular Sets

Abderrahim Jourani (1) , Emilio Vilches (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 DIM - Departamento de Ingeniería Matemática [Santiago]

The existence and the convergence (up to a subsequence) of the Moreau-Yosida regularization for the state-dependent sweeping process with nonregular (subsmooth and positively alpha-far) sets are established. Then, by a reparametrization technique, the existence of solutions for bounded variation continuous state-dependent sweeping processes with nonregular (subsmooth and positively alpha-far) sets is proved. An application to vector hysteresis is discussed, where it is shown that the Play operator with positively alpha-far sets is well defined for bounded variation continuous inputs.

Mots clés: Moreau-Yosida regularization; Subsmooth sets; Sweeping process; Positively alpha-far sets; Measure differential inclusions; Play operator; Hilbert-spaces; Bv solutions; Variational-inequalities; Differential-inclusions; Perturbation; Existence

Domaines: Mathématiques [math]

Abderrahim Jourani, Emilio Vilches. Moreau-Yosida Regularization of State-Dependent Sweeping Processes with Nonregular Sets. Journal of Optimization Theory and Applications, 2017, 173 (1), pp.91 - 116. ⟨10.1007/s10957-017-1083-6⟩. ⟨hal-01551688⟩