Abstract: The author considered the  optimal conditions and duality of Henig approximate efficient solution and Global approximate efficient solution for setvalued vector optimization problems in Banach space. Under the assumption of conesubinvex set
valued maps, the author established the sufficient optimal conditions of Henig approximate efficient solution and Global approximate efficient solution minimers and two kinds of the dual theorems of MondWeir type and Wolfe type for setvalued vector optimization problems. As an application, the author analyzed relationship between the Henig approximate efficient solution and Global approximate efficient solution minimers for setvalued vector optimization problems and two approximate efficient solution minimers for a class of vector variational inequalities.

Key words: cone-subinvex setvalued map, optimal condition, contingent derivative, approximate efficient [JP]solution, duality