SET-VALUED ORTHOGONALITY AND NEARNESS

Annamaria Barbagallo (1) , Octavian-Emil Ernst (2) , Michel Théra (3, 4)

1 University of Naples Federico II = Università degli studi di Napoli Federico II
2 AMU - Aix Marseille Université
3 DMI
4 Federation University Australia Ballarat

The theory of set-valued mappings has grown with the development of modern variational analysis. It is a key in convex and non-smooth analysis, in game theory, in mathematical economics and in control theory. The concepts of nearness and orthogonality have been known for functions since the pionnering works of Campanato and Birkhoff and James. In a recent paper [2], the authors made a connection between these two concepts. This note is mainly devoted to introduce nearness and orthogonality between set-valued mappings with the goal to study the solvability of generalized equations involving set-valued mappings.

Domaines: Optimisation et contrôle [math.OC]

Annamaria Barbagallo, Octavian-Emil Ernst, Michel Théra. SET-VALUED ORTHOGONALITY AND NEARNESS. Atti della Accademia Peloritana dei Pericolanti - Classe di Scienze Fisiche, Matematiche e Naturali, In press. ⟨hal-02472257v1⟩