A modified conjugate gradient method for optimization problems†

Abstract

An interesting refinement scheme suggested by Mehra (1909) for use with the conjugate gradient algorithm is modified and applied to both finite and infinite dimensional optimization problems in an attempt to improve the convergence rate of the algorithm. For optimal control problems, the numerical results indicate that, while the refinement scheme significantly improves the convergence rate, the improvement can often be matched by periodically restarting the algorithm.