Greedy search method for separable nonlinear models using stage Aitken gradient descent and least squares algorithms

Aitken gradient descent (AGD) algorithm takes some advantages over the standard gradient descent (SGD) and Newton methods: (1) can achieve at least quadratic convergence in general; (2) does not require the Hessian matrix inversion; (3) has less computational efforts. When using the AGD method for a...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 68; no. 8; pp. 1 - 8
Main Authors: Chen, Jing, Mao, Yawen, Gan, Min, Wang, Dongqing, Zhu, Quanmin
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Aitken acceleration technique
Algorithms
Computational modeling
Convergence
convergence rate
Cost function
Eigenvalues and eigenfunctions
Hessian matrices
hierarchical identification algorithm
Iterative algorithms
Iterative methods
Least squares
Mathematical models
Newton methods
Parameter estimation
Search methods
separable nonlinear model
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:Aitken gradient descent (AGD) algorithm takes some advantages over the standard gradient descent (SGD) and Newton methods: (1) can achieve at least quadratic convergence in general; (2) does not require the Hessian matrix inversion; (3) has less computational efforts. When using the AGD method for a considered model, the iterative function should be unchanging during all the iterations. This paper proposes a hierarchical AGD algorithm for separable nonlinear models based on stage greedy method. The linear parameters are estimated using the least squares algorithm, and the nonlinear parameters are updated based on the AGD algorithm. Since the iterative function is changing at each iteration, a stage AGD algorithm is introduced. The convergence properties and simulation examples show effectiveness of the proposed algorithm.
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content type line 14
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2022.3214474