On three-term conjugate gradient method for optimization problems with applications on COVID-19 model and robotic motion control

Ibrahim Mohammed Sulaiman,Mustafa Mamat,Poom Kumam,Aliyu Muhammed Awwal,Shadi Al-Ahmad,Maulana Malik

doi:10.1186/s13662-021-03638-9

Abstract

The three-term conjugate gradient (CG) algorithms are among the efficient variants of CG algorithms for solving optimization models. This is due to their simplicity and low memory requirements. On the other hand, the regression model is one of the statistical relationship models whose solution is obtained using one of the least square methods including the CG-like method. In this paper, we present a modification of a three-term conjugate gradient method for unconstrained optimization models and further establish the global convergence under inexact line search. The proposed method was extended to formulate a regression model for the novel coronavirus (COVID-19). The study considers the globally infected cases from January to October 2020 in parameterizing the model. Preliminary results have shown that the proposed method is promising and produces efficient regression model for COVID-19 pandemic. Also, the method was extended to solve a motion control problem involving a two-joint planar robot.

Highlights

Consider the following optimization model: min f (x), x ∈ Rn, (1.1)where f : Rn → R is a smooth function whose gradient ∇f (x) = g(x) is available
We propose a modification of Three-term Rivaie (TTRMIL)
Numerical experiments In this part, we report the numerical experiments to demonstrate the efficiency of the TTRMIL+ method in comparison with the RMIL [12], RMIL+ [13], PRP [7, 8], and TTRMIL [23] methods

Summary

Introduction

For a general function, the PRP method fails with regard to the global convergence under the Wolfe line search procedure. Convergence analysis we establish the sufficient descent condition and global convergence properties of the proposed TTRMIL+ method. The following theorem indicates that the search direction of TTRMIL+ method satisfies the sufficient descent condition. The search direction dk defined by the TTRMIL+ method always satisfies the sufficient descent condition (1.12). We will establish the global convergence of the TTRMIL+ method by first providing the following lemma to show that the standard Wolfe line search gives a lower bound for the step-size tk as follows. We present a global convergence results of the proposed TTRMIL+ CG method using the standard Wolfe line search. This disease is caused by the newly discovered coronavirus (SARS-CoV-2) and can be transmitted through droplets produced when an infected person exhales, sneezes,

F F 95 102 24 40 43 73 95 83 F 107 60 89 206 213 26 41 85 F 6 6 3 48 59 80 71

Findings

Conclusion