  Separable convex optimization problems with linear ascending inequality and
equality constraints are addressed in this paper. Under an ordering condition
on the slopes of the functions at the origin, an algorithm that determines the
optimum point in a finite number of steps is described. The optimum value is
shown to be monotone with respect to a partial order on the constraint
parameters. Moreover, the optimum value is convex with respect to these
parameters. Examples motivated by optimizations for communication systems are
used to illustrate the algorithm.
