caa a22 4500 475750330 CHVBK 20180406123521.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1023/A:1008772414083 doi (NATIONALLICENCE)springer-10.1023/A:1008772414083 Shi Yixun Department of Mathematics and Computer Science, Bloomsburg University of Pennsylvania, 17815, Bloomsburg, PA, USA aut Globally Convergent Algorithms for Unconstrained Optimization [Elektronische Daten] [Yixun Shi] A new globalization strategy for solving an unconstrained minimization problem is proposed based on the idea of combining Newton's direction and the steepest descent direction WITHIN each iteration. Global convergence is guaranteed with an arbitrary initial point. The search direction in each iteration is chosen to be as close to the Newton's direction as possible and could be the Newton's direction itself. Asymptotically the Newton step will be taken in each iteration and thus the local convergence is quadratic. Numerical experiments are also reported. Possible combination of a Quasi-Newton direction with the steepest descent direction is also considered in our numerical experiments. The differences between the proposed strategy and a few other strategies are also discussed. Kluwer Academic Publishers, 2000 unconstrained optimization nationallicence global convergence nationallicence Newton's method nationallicence Quasi-Newton method nationallicence steepest descent method nationallicence line search nationallicence Computational Optimization and Applications Kluwer Academic Publishers 16/3(2000-09-01), 295-308 0926-6003 16:3<295 2000 16 10589 https://doi.org/10.1023/A:1008772414083 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008772414083 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Shi Yixun Department of Mathematics and Computer Science, Bloomsburg University of Pennsylvania, 17815, Bloomsburg, PA, USA aut NATIONALLICENCE 773 0- Computational Optimization and Applications Kluwer Academic Publishers 16/3(2000-09-01), 295-308 0926-6003 16:3<295 2000 16 10589 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer