Characterizing Global Minimizers of the Dierence of Two Positive Valued Ane Increasing and Co-radiant Functions

Many optimization problems can be reduced to a problem with an increasing and co-radiant objective function by a suitable transformation of variables. Functions, which are increasing and co-radiant, have found many applications in microeconomic analysis. In this paper, the abstract convexity of positive valued ane increasing and co-radiant (ICR) functions are discussed. Moreover, the basic properties of this class of functions such as support set, subdi erential and maximal elements of support set are characterized. Finally, as an application, necessary and sufficient conditions for the global minimum of the dierence of two strictly positive valued ane ICR functions are presented.