  In contrast to the many continuous global optimization methods that assume
the objective function and constraints are factorable, we study how to find
globally maximal solutions to problems that are not factorable, focusing on a
particular class of problems. Specifically, we develop a method for
non-decreasing continuous submodular functions subject to constraints. We
characterize the hypograph of such functions and develop a cutting plane
algorithm that finds approximate solutions and bounds using an approximation of
the convex hull of the hypograph. We also test a spatial branch-and-bound
approach that utilizes the approximate cutting plane algorithm to form an outer
approximation and obtain upper bounds for a sub-rectangle and compare our
method with a state-of-the-art commercial solver. The main result is that for
some problems the property of submodularity is more useful than factorability.
