  In this work, the notions of normal cones at infinity to unbounded sets and
limiting and singular subdifferentials at infinity for extended real value
functions are introduced. Various calculus rules for these notions objects are
established. A complete characterization of the Lipschitz continuity at
infinity for lower semi-continuous functions is given. The obtained results are
aimed ultimately at applications to diverse problems of optimization, such as
optimality conditions, coercive properties, weak sharp minima and stability
results.
