  In this paper, we study a certain class of online optimization problems,
where the goal is to maximize a function that is not necessarily concave and
satisfies the Diminishing Returns (DR) property under budget constraints. We
analyze a primal-dual algorithm, called the Generalized Sequential algorithm,
and we obtain the first bound on the competitive ratio of online monotone
DR-submodular function maximization subject to linear packing constraints which
matches the known tight bound in the special case of linear objective function.
