Joint variable and variable projection algorithms for separable nonlinear models using Aitken acceleration technique
by Lianyuan Cheng; Jing Chen; Yingjiao Rong
International Journal of Modelling, Identification and Control (IJMIC), Vol. 42, No. 3, 2023

Abstract: This paper proposes a joint variable-based gradient descent algorithm (Joint-GD) and a variable projection (VP)-based gradient descent algorithm (VP-GD) for separable nonlinear models. The VP algorithm takes advantage of the separability property of variables to reduce the dimensionality of the parameters, which makes the convergence rates faster. In order to speed up the convergence of the gradient descent algorithm, the Aitken acceleration technique is introduced in the algorithms, which is second-order convergent. Moreover, the Aitken-based methods are robust to the step-size, therefore they can be widely used in engineering practices. The numerical simulation shows the effectiveness of the proposed algorithms.

Online publication date: Wed, 05-Apr-2023

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