Coderivatives at infinity of set-valued mappings

TL;DR

This paper introduces the concept of coderivatives at infinity for set-valued mappings, establishing well-posedness, criteria, and Fermat's rule at infinity, providing new insights even for classical smooth cases.

Contribution

It presents the first comprehensive framework for coderivatives at infinity, extending classical concepts to set-valued mappings and their asymptotic analysis.

Findings

Established well-posedness properties at infinity

Proved Mordukhovich's criterion at infinity

Provided Fermat's rule at infinity for set-valued optimization

Abstract

In this paper, the concept of coderivatives at infinity of set-valued mappings is introduced. Well-posedness properties at infinity of set-valued mappings as well as Mordukhovich's criterion at infinity are established. Fermat's rule at infinity in set-valued optimization is also provided. The obtained results, which give new information even in the classical cases of smooth single-valued mappings, provide complete characterizations of the properties under consideration in the setting at infinity of set-valued mappings.