A truncated Newton method with nonmonotone line search for unconstrained optimization
Journal of Optimization Theory and Applications
Preconditioners for indefinite systems arising in optimization
SIAM Journal on Matrix Analysis and Applications
Restarted GMRES preconditioned by deflation
Journal of Computational and Applied Mathematics
Matrix computations (3rd ed.)
Adaptively Preconditioned GMRES Algorithms
SIAM Journal on Scientific Computing
Trust-region methods
A survey of truncated-Newton methods
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Algorithm 809: PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method
ACM Transactions on Mathematical Software (TOMS)
Automatic Preconditioning by Limited Memory Quasi-Newton Updating
SIAM Journal on Optimization
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
ACM Transactions on Mathematical Software (TOMS)
On the Sensitivity of Some Spectral Preconditioners
SIAM Journal on Matrix Analysis and Applications
Iterative computation of negative curvature directions in large scale optimization
Computational Optimization and Applications
Adaptive preconditioners for nonlinear systems of equations
Journal of Computational and Applied Mathematics
Assessing a search direction within a truncated-newton method
Operations Research Letters
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We consider an iterative preconditioning technique for non-convex large scale optimization. First, we refer to the solution of large scale indefinite linear systems by using a Krylov subspace method, and describe the iterative construction of a preconditioner which does not involve matrices products or matrices storage. The set of directions generated by the Krylov subspace method is used, as by product, to provide an approximate inverse preconditioner. Then, we experience our preconditioner within Truncated Newton schemes for large scale unconstrained optimization, where we generalize the truncation rule by Nash---Sofer (Oper. Res. Lett. 9:219---221, 1990) to the indefinite case, too. We use a Krylov subspace method to both approximately solve the Newton equation and to construct the preconditioner to be used at the current outer iteration. An extensive numerical experience shows that the proposed preconditioning strategy, compared with the unpreconditioned strategy and PREQN (Morales and Nocedal in SIAM J. Optim. 10:1079---1096, 2000), may lead to a reduction of the overall inner iterations. Finally, we show that our proposal has some similarities with the Limited Memory Preconditioners (Gratton et al. in SIAM J. Optim. 21:912---935, 2011).