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 to any line-search method. In particular, we combine Newton-type directions with scaled SD steps to have suitable descent directions. Scaling the SD directions with a suitable step length makes a significant difference with respect to similar globalization approaches, in terms of both theoretical features and computational behavior. We apply our strategy to Newton's method and the BFGS method, with computational results that appear interesting compared with the results of well-established globalization strategies devised ad hoc for those methods. (C) 2020 Elsevier Inc. All rights reserved.
Using gradient directions to get global convergence of Newton-type methods
di Serafino, D;Toraldo, G;
2021
Abstract
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 to any line-search method. In particular, we combine Newton-type directions with scaled SD steps to have suitable descent directions. Scaling the SD directions with a suitable step length makes a significant difference with respect to similar globalization approaches, in terms of both theoretical features and computational behavior. We apply our strategy to Newton's method and the BFGS method, with computational results that appear interesting compared with the results of well-established globalization strategies devised ad hoc for those methods. (C) 2020 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
