FYI this algorithm is called the "Water filling algorithm" and is used extensively in Communications to optimize the allocation power for channels. You can get

FYI this algorithm is called the "Water filling algorithm" and is used extensively in Communications to optimize the allocation power for channels. You can get a solution with simple Lagrangian method (which I believe is the linear solution). http://www.eecs.berkeley.edu/~dtse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter5.pdf http://www.eecs.berkeley.edu/~dtse/Chapters_PDF/Fundamentals... (pages 183 - 185)