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

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Ibrahim Mohammed Sulaiman ◽  
Maulana Malik ◽  
Aliyu Muhammed Awwal ◽  
Poom Kumam ◽  
Mustafa Mamat ◽  
...  
Keyword(s):  
Regression Model ◽  
Motion Control ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Least Square ◽  
Optimization Models ◽  
Inexact Line Search ◽  
Novel Coronavirus

AbstractThe 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.

scholarly journals Global convergence of conjugate gradient method in unconstrained optimization problems

2019 ◽  
Vol 38 (7) ◽  
pp. 227-231
Author(s):  
Huda Younus Najm ◽  
Eman T. Hamed ◽  
Huda I. Ahmed
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Inexact Line Search ◽  
Sufficient Descent Condition ◽  
Unconstrained Optimization Problems ◽  
Sufficient Descent ◽  
Descent Condition

In this study, we propose a new parameter in the conjugate gradient method. It is shown that the new method fulfils the sufficient descent condition with the strong Wolfe condition when inexact line search has been used. The numerical results of this suggested method also shown that this method outperforms to other standard conjugate gradient method.

scholarly journals On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Min Sun ◽  
Jing Liu
Keyword(s):  
Strong Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Line Searches ◽  
Unconstrained Optimization Problems ◽  
Sufficient Descent ◽  
Large Scale Unconstrained Optimization

Recently, Zhang et al. proposed a sufficient descent Polak-Ribière-Polyak (SDPRP) conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense thatlim infk→∞∥∇f(xk)∥=0when an Armijo-type line search is used. In this paper, motivated by the line searches proposed by Shi et al. and Zhang et al., we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense thatlimk→∞∥∇f(xk)∥=0under the two new line searches. Numerical results are reported to show the efficiency of the SDPRP with the new Armijo-type line searches in practical computation.

An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and its Applications to Mechanical Design

1993 ◽  
Author(s):  
B. K. Kannan ◽  
Steven N. Kramer
Keyword(s):  
Lagrange Multiplier ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Continuous Optimization ◽  
Mixed Integer ◽  
Continuous Variables ◽  
Augmented Lagrange Multiplier

Abstract An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one and continuous variables is presented. The augmented Lagrange multiplier method combined with Powell’s method and Fletcher & Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer / discrete violations. The use of zero-one variables as a tool for conceptual design optimization is also described with an example. Several case studies have been presented to illustrate the practical use of this algorithm. The results obtained are compared with those obtained by the Branch and Bound algorithm. Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems.

scholarly journals A Penalized Linear and Nonlinear Combined Conjugate Gradient Method for the Reconstruction of Fluorescence Molecular Tomography

2007 ◽  
Vol 2007 ◽  
pp. 1-19 ◽  
Author(s):  
Shang Shang ◽  
Jing Bai ◽  
Xiaolei Song ◽  
Hongkai Wang ◽  
Jaclyn Lau
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Reconstruction Algorithms ◽  
Fluorescence Molecular Tomography ◽  
Nonlinear Conjugate Gradient Method ◽  
Gradient Based ◽  
Linear And Nonlinear

Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT.

scholarly journals A Modified Three-Term Type CD Conjugate Gradient Algorithm for Unconstrained Optimization Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Zhan Wang ◽  
Pengyuan Li ◽  
Xiangrong Li ◽  
Hongtruong Pham
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Trust Region ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
General Function ◽  
Term Type

Conjugate gradient methods are well-known methods which are widely applied in many practical fields. CD conjugate gradient method is one of the classical types. In this paper, a modified three-term type CD conjugate gradient algorithm is proposed. Some good features are presented as follows: (i) A modified three-term type CD conjugate gradient formula is presented. (ii) The given algorithm possesses sufficient descent property and trust region property. (iii) The algorithm has global convergence with the modified weak Wolfe–Powell (MWWP) line search technique and projection technique for general function. The new algorithm has made great progress in numerical experiments. It shows that the modified three-term type CD conjugate gradient method is more competitive than the classical CD conjugate gradient method.

scholarly journals A Modified Conjugacy Condition and Related Nonlinear Conjugate Gradient Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shengwei Yao ◽  
Xiwen Lu ◽  
Bin Qin
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Special Role ◽  
Conjugacy Condition ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient ◽  
The Given

The conjugate gradient (CG) method has played a special role in solving large-scale nonlinear optimization problems due to the simplicity of their very low memory requirements. In this paper, we propose a new conjugacy condition which is similar to Dai-Liao (2001). Based on this condition, the related nonlinear conjugate gradient method is given. With some mild conditions, the given method is globally convergent under the strong Wolfe-Powell line search for general functions. The numerical experiments show that the proposed method is very robust and efficient.

scholarly journals A Mixed Spectral CD-DY Conjugate Gradient Method

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Liu Jinkui ◽  
Du Xianglin ◽  
Wang Kairong
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Descent Method ◽  
Unconstrained Optimization Problems ◽  
Global Convergence Property ◽  
Wolfe Line Search ◽  
Spectral Conjugate Gradient

A mixed spectral CD-DY conjugate descent method for solving unconstrained optimization problems is proposed, which combines the advantages of the spectral conjugate gradient method, the CD method, and the DY method. Under the Wolfe line search, the proposed method can generate a descent direction in each iteration, and the global convergence property can be also guaranteed. Numerical results show that the new method is efficient and stationary compared to the CD (Fletcher 1987) method, the DY (Dai and Yuan 1999) method, and the SFR (Du and Chen 2008) method; so it can be widely used in scientific computation.

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