Quasi Matrix Free Preconditioners in Optimization and Nonlinear Least-Squares

The approximate solution of several nonlinear optimization problems requires solving sequences of symmetric linear systems. When the number of variables is large, it is advisable to use an iterative linear solver for the Newton correction step. On the other hand, the underlying linear solver can converge slowly and the calculation of a preconditioner requires the computation of the Hessian matrix which usually represents a major task in the implementation. We propose here a way to overcome at least in part this two preconditioning issue