Henig Approximate Proper Efficiency and Optimization Problems with Difference of Vector Mappings

This work focuses on approximate proper solutions of vector optimization problems. A concept of Henig approximate proper efficiency is introduced and analyzed from several points of view. First, its main properties are stated and the limit behavior in multiobjective problems of the whole Henig approximate proper efficient set is deduced. These results show that the introduced concept is suitable to approximate the efficient solution set of the problem. After that, the Henig approximate proper efficient solutions are characterized by linear scalarizations under convexity assumptions, and by ε-subgradients in optimization problems dealing with difference of vector mappings. For this last objective, a notion of ε-subdifferential is introduced and studied, obtaining, in particular, a Moreau-Rockafellar type theorem.