Proper Approximate Solutions and ε-Subdifferentials in Vector Optimization: Moreau-Rockafellar Type Theorems

We provide Moreau-Rockafellar type theorems for a kind of proper ε-subdifferential of vector-valued mappings. For this aim, we introduce and study a new notion of approximate strong solution of a vector optimization problem, a new strong ε-subdifferential based on this type of approximate strong solutions, and a new regularity condition. Finally, as a consequence of the obtained exact sum rules, the gap between the strong and the proper ε-subdifferentials is provided.