A Linesearch Algorithm with Memory for Unconstrained Optimization

This paper considers algorithms for unconstrained nonlinear optimization where the model used by the algorithm to represent the objective function explicitly includes memory of the past iterations. This is intended to make the algorithm less “myopic” in the sense that its behaviour is not completely dominated by the local nature of the objective function, but rather by a more global view. We present a non-monotone linesearch algorithm that has this feature and prove its global convergence.