Stationary points and necessary conditions in vector extremum problems

The concept of lower limit for a real-valued function is extended to vector optimization; the vector lower limit allows us to propose a definition of a vector lower semi-stationary point which extends the concept of critical Pareto point. The study of the strict connection between a lower semi-stationary point and a local vector minimum point permits us to obtain necessary and/or sufficient optimality conditions for non differentiable multiobjective functions, which assume a simple form in the differentiable case. Some of these results are characterized to Pareto vector problems and to the scalar case in order to obtain known conditions and new ones.