In the present paper, convexification strategies for certain kinds of discrete and integer non-convex optimization problems are introduced and discussed. We show how to solve problems with both posynomial and negative binomial terms in the constraints. The convexification technique may in some cases be generalized to include continuous variables. Posynomial functions are non-convex and for such functions no straightforward methods for finding the optimal solution exist. Such functions appear frequently in different kinds of chemical engineering problems. The different transformation techniques are illustrated in the form of short examples. The techniques are finally applied to a large, bilinear, trim loss problem regularly encountered at paper-converting mills.