Abstract:

In Hausdorff locally convex topological vector spaces, the concept of ε-strongly efficient subdifferential for a set-valued mapping was introduced. Under certain condition, by using the convex set separation theorem, the existence theorem for ε-strongly efficient subdifferential was proposed. As an application, the necessary optimality condition of the constraint set-valued optimization problem for ε-strongly efficient solutions was established in terms of Lagrange multiplier by using the concept of εstrongly efficient subdifferential for setvalued mapping.

Key words: ε-strong efficiency; subdifferential; Lagrange multiplier; optimality condition