In this paper, firstly, the concept of $\varepsilon-$strictly efficient subdifferential for set-valued map is introduced in Hausdorff locally convex topological vector spaces. Secondly, a characterization of this subdifferential by scalarization and the generalized $\varepsilon-$ Moreau-Rockafellar type theorem for set-valued maps are established. Finally, the necessary optimality condition of the constraint set-valued optimization problem for $\varepsilon-$ strictly efficient solutions is obtained in terms of Lagrange multiplier by using the concept of $\varepsilon-$ strictly efficient subdifferential for set-valued map.
Citation
16,Institute of Mathematics and Computer of Science, Yichun University,Yichun 336000,China;2015