  We consider the problem of maximizing a monotone nondecreasing set function
under multiple constraints, where the constraints are also characterized by
monotone nondecreasing set functions. We propose two greedy algorithms to solve
the problem with provable approximation guarantees. The first algorithm
exploits the structure of a special class of the general problem instance to
obtain a better time complexity. The second algorithm is suitable for the
general problem. We characterize the approximation guarantees of the two
algorithms, leveraging the notions of submodularity ratio and curvature
introduced for set functions. We then discuss particular applications of the
general problem formulation to problems that have been considered in the
literature. We validate our theoretical results using numerical examples.
