Preconditioned conjugate gradient methods for optimal control problems with delays with application in hydroelectric power systems scheduling

Unconstrained optimal control problems with delays in the control and state variables cannot be solved easily by Newton's method because the associated Riccati equation requires excessive computation. We consider their solution by means of preconditioned conjugate gradient methods which may be viewed as combinations of the conjugate gradient method and approximate forms of Newton's method. Experimental results suggest a rate of convergence which is intermediate between those of Newton's method and the ordinary conjugate gradient method, and a considerable overall computational advantage over these methods for many problems of interest. This work was motivated by an application in hydroelectric power systems scheduling which is described in some detail.