First and Second Order Characterizations of a Class of Pseudoconcave Vector Functions

In this paper we deeply analyze a family of vector valued pseudoconcave functions which extends to the vector case both the concepts of scalar pseudoconcavity and scalar strict pseudoconcavity, as well as the optimality properties of these functions, such as the global optimality of local optima, of critical points and of points verifying Kuhn-Tucker conditions. The considered functions come out to be particularly relevant since it is possible for them to determine several first and second order characterizations; this offers a complete extension to the vector case of the well known concept of scalar pseudoconcavity and gives the chance to work in multiobjective optimization with all the properties of the scalar case.