Vector subdifferentials and tangent cones

Abstract

Following the Rockafellar's definition for the subdifferential of a real map we define a vector subdifferential using the normal cone to the epigraph of the function. For several kinds of normal cones we have different subdifferentials; we give properties, links between them, links with addapted directional derivatives and a genaralization for the Correa Joffré Thibault and for Zagrodny theorem from the real case.

Keywords

• vector order spaces
• convex pointed normal cones
• tangent cones
• dual spaces
• Pareto optimization
• vector subdifferentials