Using gradient directions to get global convergence of Newton-type methods

The renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [2] has driven us to consider a globalization strategy based on SD, which is applicable any line-search method. In particular, we combine Newton-type directions with scaled SD steps have suitable descent directions. Scaling step length makes significant difference respect similar approaches, terms both theoretical features computational behavior. We apply our Newton’s method BFGS method, results that appear interesting compared well-established strategies devised ad hoc for those methods.