Vector subdifferentials via recession mappings

A vector subdifferential is defined for a class of directionally differentiable mappings between ordered topological vector spaces. The method used to derive the subdifferential is based on the existence of a recession mapping for a positively homogeneous operator. The properties of the recession mapping are discussed and they are shown to be similar to those in the real valued case. In addition a calculus for the vector subdifferential is developed. Finally these results are used to develop first order necessary optimality conditions for a class of vector optimization problems involvingeither proper or weak minimality concepts