  The paper considers the minimization of a separable convex function subject
to linear ascending constraints. The problem arises as the core optimization in
several resource allocation scenarios, and is a special case of an optimization
of a separable convex function over the bases of a polymatroid with a certain
structure. The paper presents a survey of state-of-the-art algorithms that
solve this optimization problem. The algorithms are applicable to the class of
separable convex objective functions that need not be smooth or strictly
convex. When the objective function is a so-called $d$-separable function, a
simpler linear time algorithm solves the problem.
