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

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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.

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Acknowledgements

The authors appreciate valuable comments and suggestions by the anonymous reviewers, which have substantially improved the quality of the paper. Furthermore, the authors acknowledge the financial support provided by the Petchra Pra Jom Klao Scholarship of King Mongkut’s University of Technology Thonburi (KMUTT) and Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. In addition, the first author was supported by the Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut’s University of Technology Thonburi (Contract No. 24/2565). Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2022 under Project No. FRB650048/0164 and National Science, Research and Innovation Fund (NSRF), King Mongkut’s University of Technology North Bangkok with Contract No. KMUTNB-FF-66-36.

Funding

Petchra Pra Jom Klao Scholarship of King Mongkut’s University of Technology Thonburi (KMUTT) and Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut’s University of Technology Thonburi (Contract No. 24/2565). Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2022 under Project No. FRB650048/0164. National Science, Research and Innovation Fund (NSRF), King Mongkut’s University of Technology North Bangkok with Contract No. KMUTNB-FF-66-36.

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Authors and Affiliations

  1. Center of Excellence in Theoretical and Computational Science (TaCS-CoE) and KMUTTFixed Point, Research Laboratory, Room SCL 802 Fixed Point Laboratory Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Mahmoud Muhammad Yahaya, Poom Kumam & Parin Chaipunya

  2. NCAO Research Center, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Parin Chaipunya

  3. Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan

    Poom Kumam

  4. Faculty of Science Energy and Environment, King Mongkut’s University of Technology North Bangkok, Rayong Campus (KMUTNB), Rayong, 21120, Thailand

    Thidaporn Seangwattana

Authors
  1. Mahmoud Muhammad Yahaya
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  2. Poom Kumam
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  3. Parin Chaipunya
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  4. Thidaporn Seangwattana
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Contributions

MMY: conceptualization, methodology, and coding; MMY: writing—original draft preparation; MMY, PC, PK: visualization, investigation, and validation; PK and PC: supervision; MMY, PC, and TS: experiment and validation; PC, TS, and PK: writing—review and editing.

Corresponding author

Correspondence to Poom Kumam.

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Communicated by Hector Cancela.

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Yahaya, M.M., Kumam, P., Chaipunya, P. et al. Structured adaptive spectral-based algorithms for nonlinear least squares problems with robotic arm modelling applications. Comp. Appl. Math. 42, 320 (2023). https://doi.org/10.1007/s40314-023-02452-1

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  • DOI: https://doi.org/10.1007/s40314-023-02452-1

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