Structured adaptive spectral-based algorithms for nonlinear least squares problems with robotic arm modelling applications

Journal article

Authors/Editors

Strategic Research Themes

Modeling Design and Optimization (Computational Science and Engineering)

Publication Details

Author list: Yahaya, Mahmoud Muhammad; Kumam, Poom; Chaipunya, Parin; Seangwattana, Thidaporn;

Publisher: Springer

Publication year: 2023

Journal acronym: Springer Nature

Volume number: 42

Issue number: 7

ISSN: 0101-8205

eISSN: 1807-0302

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85173571892&doi=10.1007%2fs40314-023-02452-1&partnerID=40&md5=40a1c219f219a4a004778d23592b39a7

Languages: English-Great Britain (EN-GB)

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Abstract

This research article develops two adaptive, efficient, structured non-linear least-squares algorithms, NLS. The approach taken to formulate these algorithms is motivated by the classical Barzilai and Borwein (BB) (IMA J Numer Anal 8(1):141–148, 1988) parameters. The structured vector approximation, which is an action of a vector on a matrix, is derived from higher order Taylor series approximations of the Hessian of the objective function, such that a quasi-Newton condition is satisfied. This structured approximation is incorporated into the BB parameters’ weighted adaptive combination. We show that the algorithm is globally convergent under some standard assumptions. Moreover, the algorithms’ robustness and effectiveness were tested numerically by solving some benchmark test problems. Finally, we apply one of the algorithms to solve a robotic motion control model with three degrees of freedom, 3DOF. © 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.

Keywords

Non-monotone line search