Accelerated conjugate gradient algorithm with finite difference Hessian/vector product approximation for unconstrained optimization

In this paper we propose a fundamentally different conjugate gradient method, in which the well-known parameter βk is computed by an approximation of the Hessian/vector product through finite differences. For search direction computation, the method uses a forward difference approximation to the Hessian/vector product in combination with a careful choice of the finite difference interval. For the step length computation we suggest an...