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

Ibrahim Mohammed Sulaiman1, Maulana Malik2, Aliyu Muhammed Awwal3,4,5

  • 1Department of Mathematics and Statistics, School of Quantitative Sciences, College of Art and Sciences (CAS), Universiti Utara Malaysia (UUM), 06010 Sintok, Kedah Malaysia.

Advances in Continuous and Discrete Models
|April 22, 2022
PubMed
Summary

A modified three-term conjugate gradient method enhances unconstrained optimization and regression modeling. This efficient algorithm shows promise for modeling the COVID-19 pandemic and robot motion control.

Keywords:
Coronavirus (COVID-19)Finite differenceLine search procedureMotion controlOptimization modelsRegression analysisThree-term CG algorithms

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Area of Science:

  • Numerical Analysis
  • Optimization
  • Computational Statistics

Background:

  • Three-term conjugate gradient (CG) algorithms offer efficiency and low memory usage for optimization.
  • Regression models, often solved with least squares and CG-like methods, describe statistical relationships.

Purpose of the Study:

  • To present a modified three-term conjugate gradient method for unconstrained optimization.
  • To establish global convergence properties under inexact line search.
  • To apply the modified method to regression modeling for COVID-19 and robotics.

Main Methods:

  • Modification of a standard three-term conjugate gradient algorithm.
  • Inexact line search for establishing global convergence.
  • Application to parameterize a COVID-19 regression model using global infection data.
  • Extension to a motion control problem for a two-joint planar robot.

Main Results:

  • The modified CG method demonstrates global convergence under inexact line search.
  • The method successfully parameterized a regression model for COVID-19 cases (January-October 2020).
  • Preliminary results indicate the method's efficiency and promise for pandemic modeling and robot control.

Conclusions:

  • The proposed modified three-term conjugate gradient method is effective for unconstrained optimization.
  • The algorithm provides an efficient approach for developing regression models, notably for the COVID-19 pandemic.
  • The method's applicability extends to complex problems like robot motion control.