Conjugate gradient search in the initial costate space

The conjugate gradient algorithm of Fletcher and Reeves (1964) has recently been fruitfully incorporated in the numerical solution of optimal control problems. Unlike others who apply the algorithm as a searching mechanism in function space, this correspondence demonstrates the effectiveness of the algorithm as a tool for searching in the initial costate space. The technique presented herein is the penalty function approach suggested by Knapp and Frosts (ibid., voL AC-IO. pp. 189-193. April 1965) coupled with a conjugate gradient search.