A Bolza problem in hydrothermal optimization

This paper studies the optimization of large-scale hydrothermal power systems. For the general problem with n hydro-plants, we present an algorithm using a particular strategy related to the Gauss-Southwell method of nonlinear optimization. The algorithm offers a constructive method for producing sequences of problems with one hydro-plant. For this simple problem we use Pontryagin's minimum principle to prove a condition for the extremals of the functional. We set out our problem in terms of optimal control in continuous time, with the Bolza-type functional. Finally, we present one example employing a program developed with the “Mathematica” package and analyze the convergence of the algorithm.