Damped Inexact Quasi-Newton Methods

The inexact quasi-Newton methods are very attractive methods for large scale optimization since they require only an approximate solution of the linear system of equations for each iteration. To achieve global convergence results, we adjust the step using a backtracking strategy. We discuss the backtracking strategy in detail and show that this strategy has similar convergence properties as one obtains by using line searches with the Goldstein-Armijo conditions. The combination of backtracking and inexact quasi-Newton methods is particularly attractive since the conditions for convergence are easily met. We give conditions for Q-linear and Q-superlinear convergence