An improved accelerated 3-term conjugate gradient algorithm with second-order Hessian approximation for nonlinear least-squares optimization

Volume 36, Issue 3, pp 263--274 https://dx.doi.org/10.22436/jmcs.036.03.02

Publication Date: August 06, 2024 Submission Date: April 19, 2024 Revision Date: June 07, 2024 Accteptance Date: June 29, 2024

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Authors

R. B. Yunus - Department of Fundamental and Applied Sciences‎, ‎Faculty of Science and Information Technology, ‎Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, ‎Perak Darul Ridzuan, ‎Malaysia. N. Zainuddin - Department of Fundamental and Applied Sciences‎, ‎Faculty of Science and Information Technology, ‎Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, ‎Perak Darul Ridzuan, ‎Malaysia. H. Daud - Department of Fundamental and Applied Sciences‎, ‎Faculty of Science and Information Technology, ‎Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, ‎Perak Darul Ridzuan, ‎Malaysia. R. Kannan - Department of Electrical and Electronics Engineering, ‎Universiti Teknologi PETRONAS, ‎Bandar Seri Iskandar 32610, ‎Perak Darul Ridzuan, ‎Malaysia. M. M. Yahaya - 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. A. Al-Yaari - Department of Fundamental and Applied Sciences‎, ‎Faculty of Science and Information Technology, ‎Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, ‎Perak Darul Ridzuan, ‎Malaysia.

Abstract

‎Nonlinear least-squares (NLS) problems find extensive applications across various fields within the applied sciences‎. ‎Conventional methods for solving NLS problems often face challenges related to computational efficiency and memory requirements‎, ‎especially when dealing with large-scale systems‎. ‎In this paper‎, ‎the solution to the minimization of nonlinear least squares problems has been obtained using a proposed structured accelerated three-term conjugate gradient method‎, ‎in which from Taylor series approximations of the objective function's Hessian‎, ‎the structured vector approximation involving a vector's action on a matrix is obtained‎. ‎This ensures the satisfaction of a quasi-Newton condition‎. ‎The technique then employs the structured vector approximation to incorporate additional information from the Hessian of the goal function into the standardized search direction‎. ‎The proposed method's search direction fulfills the necessary descent criterion‎. ‎Additionally‎, ‎numerical tests performed on various test problems show that the suggested approach is remarkably efficient‎, ‎surpassing some existing competitors‎.

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Keywords

• Three-term
• nonlinear
• least-squares
• accelerated
• conjugate gradient

MSC

•  65K05‎
•  ‎65K10

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