Optimal Algorithms and the BFGS Updating Techniques for Solving Unconstrained Nonlinear Minimization Problems
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-03-12
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
To solve an unconstrained nonlinear minimization problem, we propose an optimal algorithm (OA) as well as a globally optimal algorithm (GOA), by deflecting the gradient direction to the best descent direction at each iteration step, and with an optimal parameter being derived explicitly.
An invariant manifold defined for the model problem in terms of a locally quadratic function is used to derive a purely iterative algorithm and the convergence is proven.
Then, the rank-two updating techniques of BFGS are employed, which result in several novel algorithms as being faster than the steepest descent method (SDM) and the variable metric method (DFP).
Six numerical examples are examined and compared with exact solutions, revealing that the new algorithms of OA, GOA, and the updated ones have superior computational efficiency and accuracy.
American Psychological Association (APA)
Liu, Chein-Shan. 2014. Optimal Algorithms and the BFGS Updating Techniques for Solving Unconstrained Nonlinear Minimization Problems. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-14.
https://search.emarefa.net/detail/BIM-463504
Modern Language Association (MLA)
Liu, Chein-Shan. Optimal Algorithms and the BFGS Updating Techniques for Solving Unconstrained Nonlinear Minimization Problems. Journal of Applied Mathematics No. 2014 (2014), pp.1-14.
https://search.emarefa.net/detail/BIM-463504
American Medical Association (AMA)
Liu, Chein-Shan. Optimal Algorithms and the BFGS Updating Techniques for Solving Unconstrained Nonlinear Minimization Problems. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-14.
https://search.emarefa.net/detail/BIM-463504
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-463504