M.: Preconditioning Newton-Krylov methods in nonconvex large scale optimization. Report DIS 01-2007, Dipartimento di Informatica e Sistemistica ”A. Ruberti” SAPIENZA - Universita di

We consider an iterative preconditioning technique for large scale optimization, where the objective function is possibly non-convex. First, we refer to the solution of a generic indef-inite linear system by means of a Krylov subspace method, and describe the iterative construction of the preconditioner which does not involve matrices products or matrix stor-age. The set of directions generated by the Krylov sub-space method is also used, as by product, to provide an approximate inverse of the system matrix. Then, we ex-perience our method within Truncated Newton schemes for large scale unconstrained optimization, in order to speed up the solution of the Newton equation. Actually, we use a Krylov subspace method to approximately solve the New-ton equation at current iterate (where the Hessian matrix is possibly indefinite) and to construct the preconditioner to be used at the current outer iteration. An extensive nu-merical experience show that the preconditioning strategy proposed leads to a significant reduction of the overall inner iterations on most of the test problems considered.