A method and apparatus for controlling the pump powers of a broadband DWDM optical system using Raman amplification which determines pump settings that are advantageously directed to minimizing the peak-to-peak ripple of the channel powers with respect to a given per-channel target. The illustrative method and apparatus first formulates a linear programming optimization problem, and then solves the formulated linear program in order to derive a new set of pump powers to be applied to the Raman amplification pumps. In accordance with the principles of the invention, the formulated linear programming optimization problem advantageously includes one or more "virtual" channels in addition to the actual channels used in the optical transmission system. The linear program may be solved with use of any conventional linear programming solution technique, such as, for example, the simplex method.