Quasi–Newton updates for Preconditioned Nonlinear Conjugate Gradient methods

In this paper we study new preconditioners for the Nonlinear Conjugate Gradient (NCG) method in large scale unconstrained optimization. Our preconditioners are based on quasi--Newton updates, which approximate the inverse of the Hessian matrix. In particular, we consider a couple of new low-rank quasi-Newton symmetric updating formulae. Some preliminary numerical experiences are carried on, showing a comparison between one of our proposals and the use of L-BFGS update as preconditioner