An Approximate Inverse Preconditioner in Truncated Newton Methods for Large Scale Optimization

Giovanni Fasano, Massimo Roma


This work considers the use of truncated Newton methods for the solution of large
scale unconstrained optimization problems. Two key aspects of truncated Newton methods
may be still considered open questions: how to handle the case with indefinite Hessian
and how to formulate a general effective preconditioning strategy. We propose the use
of Conjugate Gradient-based schemes as a tool for facing up to both the questions.
These schemes can be successfully used for computing an efficient Newton-type direction
whenever the Hessian is indefinite. Furthermore they enable to define a suitable approximate
inverse preconditioning technique for reducing the overall inner iterations.

[DOI: 10.1685 / CSC06076] About DOI

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