A new generalized quasi-Newton algorithm based on structured diagonal Hessian approximation for solving nonlinear least-squares problems with application to 3DOF planar robot arm manipulator
Journal article
Authors/Editors
Strategic Research Themes
Publication Details
Author list: Yahaya M.M., Kumam P., Awwal A.M., Chaipunya P., Aji S., Salisu S.
Publisher: Institute of Electrical and Electronics Engineers
Publication year: 2022
Volume number: 10
Start page: 10816
End page: 10826
Number of pages: 11
ISSN: 2169-3536
eISSN: 2169-3536
Languages: English-Great Britain (EN-GB)
View in Web of Science | View on publisher site | View citing articles in Web of Science
Abstract
Many problems in science and engineering can be formulated as nonlinear least-squares (NLS) problems. Thus, the need for efficient algorithms to solve these problems can not be overemphasized. In that sense, we introduce a generalized structured-based diagonal Hessian algorithm for solving NLS problems. The formulation associated with this algorithm is essentially a generalization of a similar result in Yahaya et al. (Journal of Computational and Applied Mathematics, pp. 113582, 2021). However, in this work, the structured diagonal Hessian update is derived under a weighted Frobenius norm; this allows other choices of the weighted matrix analogous to the Davidon-Fletcher-Powell (DFP) method. Moreover, to theoretically fill the gap in Yahaya et al. (Journal of Computational and Applied Mathematics, pp. 113582, 2021), we have shown that the proposed algorithm is R-linearly convergent under some standard conditions devoid of any safeguarding strategy. Furthermore, we experimentally tested the proposed scheme on some standard benchmark problems in the literature. Finally, we applied this algorithm to solve robotic motion control problem consisting of 3DOF (degrees of freedom). Author
Keywords
Approximation algorithms, diagonal updating, least change secant, quasi-Newton, robotic motion control, Robot motion, Taylor series
Contact Information