ε-Optimality Conditions for Vector Optimization Problems with Set-Valued Maps
Lê Anh Tuấn · Numerical Functional Analysis and Optimization · 2010
In this paper, I introduce two kinds of ε-subgradients—ε-Pareto subgradients and ε-Benson proper subgradients—for set-valued maps. I give sufficient conditions for the existence of such ε-subgradients. A generalized ε-Moreau–Rockafellar type theorem for ε-Benson proper subdifferentials of set-valued maps is formulated and applied to establish ε-optimality conditions for ε-Benson proper efficient solutions of vector optimization problems with set-valued maps. Scalarization theorems for such a problem are also obtained.