On the steplength selection in gradient methods for unconstrained optimization

The seminal paper by Barzilai and Borwein (1988) has given rise to an extensive investigation, leading to the development of effective gradient methods. Several steplength rules have been first designed for unconstrained quadratic problems and then extended to general nonlinear optimization problems. These rules share the common idea of attempting to capture, in an inexpensive way, some second-order information. However, the convergence theory...