Adjustment of the scaling parameter of Dai-Kou type conjugate gradient methods with application to motion control

Mahbube Akbari; Saeed Nezhadhosein; Aghile Heydari

Applications of Mathematics (2024)

  • Volume: 69, Issue: 6, page 829-845
  • ISSN: 0862-7940

Abstract

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We introduce a new scaling parameter for the Dai-Kou family of conjugate gradient algorithms (2013), which is one of the most numerically efficient methods for unconstrained optimization. The suggested parameter is based on eigenvalue analysis of the search direction matrix and minimizing the measure function defined by Dennis and Wolkowicz (1993). The corresponding search direction of conjugate gradient method has the sufficient descent property and the extended conjugacy condition. The global convergence of the proposed algorithm is given for both uniformly convex and general nonlinear objective functions. Also, numerical experiments on a set of test functions of the CUTER collections and the practical problem of the manipulator of robot movement control show that the proposed method is effective.

How to cite

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Akbari, Mahbube, Nezhadhosein, Saeed, and Heydari, Aghile. "Adjustment of the scaling parameter of Dai-Kou type conjugate gradient methods with application to motion control." Applications of Mathematics 69.6 (2024): 829-845. <http://eudml.org/doc/299649>.

@article{Akbari2024,
abstract = {We introduce a new scaling parameter for the Dai-Kou family of conjugate gradient algorithms (2013), which is one of the most numerically efficient methods for unconstrained optimization. The suggested parameter is based on eigenvalue analysis of the search direction matrix and minimizing the measure function defined by Dennis and Wolkowicz (1993). The corresponding search direction of conjugate gradient method has the sufficient descent property and the extended conjugacy condition. The global convergence of the proposed algorithm is given for both uniformly convex and general nonlinear objective functions. Also, numerical experiments on a set of test functions of the CUTER collections and the practical problem of the manipulator of robot movement control show that the proposed method is effective.},
author = {Akbari, Mahbube, Nezhadhosein, Saeed, Heydari, Aghile},
journal = {Applications of Mathematics},
keywords = {unconstrained optimization problem; self-scaling memoryless BFGS; conjugate gradient; measure function},
language = {eng},
number = {6},
pages = {829-845},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Adjustment of the scaling parameter of Dai-Kou type conjugate gradient methods with application to motion control},
url = {http://eudml.org/doc/299649},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Akbari, Mahbube
AU - Nezhadhosein, Saeed
AU - Heydari, Aghile
TI - Adjustment of the scaling parameter of Dai-Kou type conjugate gradient methods with application to motion control
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 6
SP - 829
EP - 845
AB - We introduce a new scaling parameter for the Dai-Kou family of conjugate gradient algorithms (2013), which is one of the most numerically efficient methods for unconstrained optimization. The suggested parameter is based on eigenvalue analysis of the search direction matrix and minimizing the measure function defined by Dennis and Wolkowicz (1993). The corresponding search direction of conjugate gradient method has the sufficient descent property and the extended conjugacy condition. The global convergence of the proposed algorithm is given for both uniformly convex and general nonlinear objective functions. Also, numerical experiments on a set of test functions of the CUTER collections and the practical problem of the manipulator of robot movement control show that the proposed method is effective.
LA - eng
KW - unconstrained optimization problem; self-scaling memoryless BFGS; conjugate gradient; measure function
UR - http://eudml.org/doc/299649
ER -

References

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