  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.
