Inertial-Based Derivative-Free Method for System of Monotone Nonlinear Equations and Application

Aliyu Muhammed Awwal,Poom Kumam,Lin Wang,Wiyada Kumam,Shuang Huang

doi:10.1109/access.2020.3045493

Abstract

Iterative methods for solving nonlinear problems are of great importance due to their appearance in various areas of applications. In this paper, based on the inertial effect, we propose two projection derivative-free iterative methods for solving system of nonlinear equations. For the purpose of improving the numerical performance, the two methods incorporated the inertial step into the modified Barzilai and Borwein (BB) spectral parameters to generate the sequence of their respective search directions. The two spectral parameters are shown to be well-defined. For each method, the sequence of the search direction is bounded and satisfies the sufficient descent property. We establish the convergence analysis of the two methods based on the assumption that the underlying mapping is Lipschitzian and monotone. We demonstrate the efficiencies of the two methods on some collection of monotone system of nonlinear equations test problems. Finally, we apply the two methods to solve motion control problem involving a two planar robot.

Highlights

Let Λ be a nonempty closed and convex subset of an n−dimensional Euclidean space Rn
We propose two inertial-based spectral algorithms for solving system of monotone nonlinear equations with convex constraints based on the projection technique
We implement these algorithms to solve a collection of monotone system of nonlinear equations, see Test Problems

Summary

Introduction

Let Λ be a nonempty closed and convex subset of an n−dimensional Euclidean space Rn. Let ·, · and · , respectively, denote the inner product and Euclidean norm in Rn. INDEX TERMS inertial effect, line search, nonlinear monotone equations, nonlinear problems, numerical algorithms, projection method, spectral parameters Question: Can the inertial effect speeds up the numerical performance of the derivative-free spectral iterative algorithm for system of nonlinear equations?

Results

Conclusion