In this study, we discuss on the problem of minimizing the differences of two non-positive valued
increasing, co-radiant and quasi-concave (ICRQC) functions defined on X (where X is a real locally convex
topological vector space). For this purpose, we first gave different characterizations of the upper support set’s
minimal elements of non-positive co-radiant functions. Then, we presented sufficient and necessary conditions
for the global minimizers of the differences of two non-positive ICRQC functions.