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.
Quasi–Newton updates for Preconditioned Nonlinear Conjugate Gradient methods
FASANO, Giovanni;
2012-01-01
Abstract
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.
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