Modified Newton integration algorithm with noise suppression for online dynamic nonlinear optimization
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Modified Newton integration algorithm with noise suppression for online dynamic nonlinear optimization Haoen Huang1 · Dongyang Fu1 · Guancheng Wang2 · Long Jin3,4,5 · Shan Liao6 · Huan Wang1 Received: 29 November 2019 / Accepted: 2 July 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The solution of nonlinear optimization is usually encountered in many fields of scientific researches and engineering applications, which spawns a large number of corresponding algorithms to cope with it. Besides, with developments of modern cybernetics technology, it imperatively requires some advanced numerical algorithms to solve online dynamic nonlinear optimization (ODNO). Nevertheless, the major existing algorithms are limited to the static nonlinear optimization models, few works considering the dynamic ones, let alone tolerating noise. For the abovementioned reasons, this paper proposes a modified Newton integration (MNI) algorithm for ODNO with strong robustness and high-accuracy computing solution, which can effectively suppress the influence caused by noise components. In addition, the correlative theoretical analyses and mathematical proofs on convergence and robustness of the MNI algorithm are carried out, which indicates that computing solutions of the proposed MNI algorithm can globally converge to relative small value in the presence of various noise or zero noise conditions. Finally, to illustrate the advantages and feasibilities of the proposed MNI algorithm for ODNO problems, four numerical simulation examples and an application to robot manipulator motion generation are performed. Keywords Online dynamic nonlinear optimization (ODNO) · Modified Newton integration (MNI) algorithm · Noise-suppressing · Steady-state error
Dongyang Fu
[email protected]
Extended author information available on the last page of the article.
Numerical Algorithms
1 Introduction As an extraordinarily significant branch in optimization field, nonlinear optimization problems have appeared in various fields of scientific researches and engineering applications [1–4], including image processing [5], path planning [6], robotic control [7], and other technologies [8–11]. Broadly speaking, due to its pivotal roles, researchers have established systematic schemes and constructed a series of algorithms for various nonlinear optimization problems [12–14]. It is worth noting that exploiting gradient-type methods to handle nonlinear optimization is an effective way. For instance, in [15], Li et al. provide a conjugate gradient method for weight unconstrained optimization, where the global convergence is proved. Besides, some modified scaled nonlinear conjugate gradient methods are presented by Dehghani et al. [16] who also prove that effectiveness of their algorithms is prominent on nonzero residuals. In addition, based on Andrei’s approach, a modified scaled memoryless conjugate gradient method is addressed in [17], where the method is confirmed to be of global convergence without convexity on the cost function
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