Global minimization of the difference of increasing co-radiant and quasi-concave functions

Functions which are increasing, co-radiant and quasi-concave have found many applications in microeconomic analysis. In production theory it is commonly assumed that the production function is increasing and quasi-concave. Likewise in consumer theory one often assumes that the utility function has these properties. In this paper, we first examine characterizations of the dual problem for the difference of two increasing, co-radiant and quasi-concave functions. Next, we give various characterizations of the minimal elements of the upper support set of co-radiant functions, by applying a type of duality, which is used in microeconomic theory. As an application, we obtain necessary and sufficient conditions for the global minimum of the difference of two increasing, co-radiant and quasi-concave functions defined on a real locally convex topological vector space X.