Algorithms for separable convex optimization with linear ascending constraints

Abstract

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 generalizes a prior algorithm to a wider class of separable convex objective functions that need not be smooth or strictly convex. The paper also summarizes the state-of-the-art algorithms that solve this optimization problem. When the objective function is a so-called \(d{\text {-}}\)separable function, a simpler linear time algorithm solves the problem.