Prox-regularity approach to generalized equations and image projection

Samir Adly (1) , Florent Nacry (1) , Lionel Thibault (2)

1 XLIM-MATHIS - Mathématiques & Sécurité de l'information
2 IMAG - Institut Montpelliérain Alexander Grothendieck

In this paper, we first investigate the prox-regularity behaviour of solution mappings to generalized equations. This study is realized through a nonconvex uniform Robinson−Ursescu type theorem. Then, we derive new significant results for the preservation of prox-regularity under various and usual set operations. The role and applications of prox-regularity of solution sets of generalized equations are illustrated with dynamical systems with constraints.

Mots clés: Nonsmooth dynamics; Variational inclusion; Variational analysis; Prox-regular set; Metric regularity; Generalized equation; Robinson−Ursescu Theorem

Domaines: Mathématiques [math]

Samir Adly, Florent Nacry, Lionel Thibault. Prox-regularity approach to generalized equations and image projection. ESAIM: Control, Optimisation and Calculus of Variations, 2018, 24 (2), pp.677-708. ⟨10.1051/cocv/2017052⟩. ⟨hal-02072430⟩