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Adjustment of the scaling parameter of Dai-Kou type conjugate gradient methods with application to motion control
Applications of Mathematics, Tome 69 (2024) no. 6, pp. 829-845 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2024.0006-24
Classification : 65K99, 90C06, 90C53
Keywords: unconstrained optimization problem; self-scaling memoryless BFGS; conjugate gradient; measure function 
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Akbari, Mahbube; Nezhadhosein, Saeed; Heydari, Aghile. Adjustment of the scaling parameter of Dai-Kou type conjugate gradient methods with application to motion control. Applications of Mathematics, Tome 69 (2024) no. 6, pp. 829-845. doi: 10.21136/AM.2024.0006-24

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