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

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.

Modified spectral conjugate gradient iterative scheme for unconstrained optimization problems with application on COVID-19 model

“…In recent times, several works of literature have employed different mathematical and numerical approaches for modeling the COVID-19 outbreak [see [5,32,52]]. This paper aims to study the performance of the proposed method on a parameterized COVID-19 regression model.…”

“…Based on several works of literature, the linear regression process rarely occurs in situations because most problems are often nonlinear in nature. Based on the non-linearity of the problems, studies usually consider the nonlinear regression process [5]. This and other considerations motivated the idea of using the nonlinear regression procedure in this study.…”

“…Now, we can apply the proposed method to solve the model (25). The results presented in Table 4 illustrate the performance of the proposed FMSD algorithm for problem (25) under the weak Wolfe line search conditions (4)(5).…”

“…For instance, Aggarwal et al [3] proposed a partial differential equation model to calculate the number of COVID-19 cases in Punjab by using the modified cubic B-spline function and differential quadrature method. Other numerical methods which are applied to solve the COVID-19 model were proposed by Amar et al [4] and Sulaiman et al [5]. Amar et al used various statistics and machine learning modeling approaches to forecast the COVID-19 spread in Egypt.…”

“…The CG method has recently been used to solve various problems related to optimization. For example, image reconstruction [23][24][25], compressed sensing [26], signal processing [27], robotic motion control [5,15,16,28,29], portfolio selection [5,13,14,[29][30][31], regression analysis [5,32] and many more.…”