Minimizing the Difference of Dual Functions of Two Coradiant Functions

In this article, we solve the problem of minimizing the difference of dual functions of two coradiant functions. We do this by applying a type of duality, that is used in microeconomic theory. Indeed, the dual function of a co-radiant function is decreasing and inverse coradiant. So, we first give various characterizations for the maximal elements of the support sets of this class of functions. Next, by using these results, we obtain the necessary and sufficient conditions for the global minimizers of the difference of two decreasing and inverse coradiant functions. Finally, as an application, we present the necessary and sufficient conditions for the global minimizers of the difference of dual functions of two co-radiant functions.