This paper analyzes the mathematical properties related to the hydro-power generation optimization problem. From the problem's physical nature, it can be concluded that the hydro-power generation is a function of the plant productivity and the water discharge. Since the plant productivity must be an increasing function of the net height, it was shown, under mild conditions, that the resulting generation is a strongly increasing function. Given that, it was established some mathematical properties that guarantee a unique maximum inside the feasible set and, therefore, global optimality. Under this analysis it is possible to derive optimization problems with optimality guarantees. Finally, a problem concerning the minimization of the deficit between supply and demand during a time window for a single power plant is explored. A numerical example based on a real case is given. Other existing formulations could also take advantage of our main results to confirm global optimality or to prove multimodality. These results are also useful to define the best optimization strategies for a given optimization problem. (C) 2014 Elsevier Ltd. All rights reserved.