Global convergence properties of conjugate gradient methods for optimal control problems

The conjugate gradient technique has been broadly used to solve various unconstrained problems. In this paper, we present an extension of a nonlinear conjugate gradient algorithm for the solution of nonlinear optimal control problems with different parameters. Firstly, we converted the optimal control problems to an unconstrained form by the gradient trajectory of Hamilton function. Then we propose a different conjugate gradient parameter β_k, and the corresponding method successfully generates a sufficient descent direction independent of the Wolfe conditions employed. In addition, the global weak and strong convergence properties of the conjugate gradient approach with this parameter are obtained under a guaranteed descent and an efficient line search. Finally, the numerical experiment results show that the proposed method can efficiently solve the nonlinear optimal control problem and therefore is promising.