Greedy Search Method for Separable Nonlinear Models Using Stage Aitken Gradient Descent and Least Squares Algorithms

Abstract

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.