Computing an integer point of a class of convex sets

A simplicial algorithm is proposed for computing an integer point of a convex set C subset of R-n satisfying chi = max {chi (1), chi (2)} = (max {chi (1)(1), chi (2)(1)}, ... , max {chi (1)(n),chi (2)(n)})(T) is an element of C, with chi (1) = (chi (1)(1), chi (1)(2), ... , chi (1)(n))(T) is an element of C, chi (2) = (chi (2)(1), chi (2)(2), ... , chi (2)(n))(T) is an element of C. The algorithm subdivides R-n into integer simplices and assigns an integer label to each integer point of R-n. Starting at an arbitrary integer point, the algorithm follows a finite simplicial path that leads either to an integer point of C or to the conclusion that C has no integer point.