Higher-Order Conjugate Gradient Method (HCGM) For Solving Continuous Optimal Control Problems

In this paper, we considered the role of penalty when the higher-order conjugate gradient method (HCGM) was used as a computational scheme for the minimization of penalised cost functions for optimal control problems described by linear systems and integral quadratic costs. For this family of commonly encountered problems, we find out that the conventional penalty methods require very large penalty constants for good constants satisfaction. Numerical results shows that, as the penalty constant tend to infinity, the convergence rate of the method becomes poor. To circumvent the poor convergence rate of the penalty method, the HCGM was often considered as a good substitute to accelerate the convergence.