Article ID: | iaor20132830 |
Volume: | 157 |
Issue: | 2 |
Start Page Number: | 462 |
End Page Number: | 485 |
Publication Date: | May 2013 |
Journal: | Journal of Optimization Theory and Applications |
Authors: | Hilout Sad, Argyros Ioannis |
Keywords: | heuristics |
A semilocal convergence analysis for directional Secant‐type methods in multidimensional space is provided. Using weaker hypotheses than the ones exploited by An and Bai, we provide a semilocal convergence analysis with the following advantages: weaker convergence conditions, larger convergence domain, finer error estimates on the distances involved, and more precise information on the location of the solution. A numerical example, where our results apply to solve an equation but not the ones of An and Bai, is also provided. In a second example, we show how to implement the method.