ON THE INTERSECTION OF 2 PARTICULAR CONVEX-SETS

In this note, necessary and sufficient conditions are given for the in tersection of the m(-1) simplex co{xi(1),...,xi(m)} of m affinely inde pendent vectors xi(1),...,xi(m) of R(n) and the negative orthant R-(n) to be empty, i.e., co{xi(1),...,xi(m)} boolean AND R-(n)=<empty set>, where m less than or equal to n. It is also shown that the special ca se m=2 can be checked easily. These results suggest that the above-men tioned emptiness can be checked recursively. Some numerical examples a re given to illustrate the results. Potential applications of these re sults include the compatible multicommodity flow problems and satisfic ing solution problems.