Super-efficiency of vector optimization in Banach spaces

Using variational analysis, in terms of the Clarke normal cone, we consider super-efficiency of vector optimization in Banach spaces. We establish some characterizations for super-efficiency. In particular, dropping the assumption that the ordering cone has a bounded base, we extend a result in Borwein and Zhuang [J.M. Borwein, D. Zhuang, Super-efficiency in vector optimization, Trans. Amer. Math. Soc. 338 (1993) 105–122] to the nonconvex setting.