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.
Vector subdifferentials via recession mappings / Zaffaroni, Alberto; Glover,. - In: OPTIMIZATION. - ISSN 0233-1934. - STAMPA. - 39:(1997), pp. 203-237.
Vector subdifferentials via recession mappings
ZAFFARONI, Alberto;
1997
Abstract
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.
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