An improved approach of Armijo-based adaptive stability transformation method

Abstract

The Armijo-based adaptive stability transformation method (AASTM) can improve the convergence of the algorithm by adaptive selection of chaos control factor in the iteration process. But, AASTM has the problem of small step iteration in the iteration process when it is not fit for Armijo criterion. It greatly affects the computational efficiency. Therefore, based on the theory of AASTM, an improved adaptive stability method based on iteration angle is proposed in this paper. The method controls the iteration process by allowable iteration angle, and reselects the chaos control factor when the Armijo criterion fails, so as to relax the step size. At the same time, it studies the iteration under different allowable iteration angles and gives the optimal value of the allowable iteration angle. The proposed method not only retains the advantage of AASTM in adaptive step selection, but also solves the small step iteration problem of AASTM in the iteration process. Six examples are given and show that the method proposed in this paper has obvious advantages in terms of computational efficiency and stability.