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

被引：0
作者：
Mahmoud Muhammad Yahaya
Poom Kumam
Parin Chaipunya
Thidaporn Seangwattana
机构：
[1] King Mongkut’s University of Technology Thonburi (KMUTT),Center of Excellence in Theoretical and Computational Science (TaCS
[2] King Mongkut’s University of Technology Thonburi (KMUTT),CoE) and KMUTTFixed Point, Research Laboratory, Room SCL 802 Fixed Point Laboratory Science Laboratory Building, Department of Mathematics, Faculty of Science
[3] China Medical University,NCAO Research Center, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS
[4] King Mongkut’s University of Technology North Bangkok,CoE)
来源：
Computational and Applied Mathematics | 2023年 / 42卷
关键词：
Spectral gradient method; Non-monotone line search; Non-linear least squares; 93E24; 90C30; 65K05; 49M37;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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