On q-variant of Dai–Yuan conjugate gradient algorithm for unconstrained optimization problems

2021 ◽  
Author(s):  
Shashi Kant Mishra ◽  
Mohammad Esmael Samei ◽  
Suvra Kanti Chakraborty ◽  
Bhagwat Ram
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Optimization Problems ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Unconstrained Optimization Problems

scholarly journals A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shashi Kant Mishra ◽  
Suvra Kanti Chakraborty ◽  
Mohammad Esmael Samei ◽  
Bhagwat Ram
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Test Problems ◽  
Conjugate Gradient Algorithms ◽  
Gradient Algorithms ◽  
Unconstrained Optimization Problems ◽  
Wolfe Conditions ◽  
Nonlinear Unconstrained Optimization

AbstractA Polak–Ribière–Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a q-variant of the PRP (q-PRP) method for which both the sufficient and conjugacy conditions are satisfied at every iteration. The proposed method is convergent globally with standard Wolfe conditions and strong Wolfe conditions. The numerical results show that the proposed method is promising for a set of given test problems with different starting points. Moreover, the method reduces to the classical PRP method as the parameter q approaches 1.

scholarly journals A new hybrid conjugate gradient algorithm for unconstrained optimization with inexact line search

2020 ◽  
Vol 20 (2) ◽  
pp. 939
Author(s):  
Fanar N. Jardow ◽  
Ghada M. Al-Naemi
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Convex Combination ◽  
Gradient Algorithm ◽  
Inexact Line Search ◽  
Unconstrained Optimization Problems ◽  
Large Scale Unconstrained Optimization

Many researchers are interested for developed and improved the conjugate gradient method for solving large scale unconstrained optimization problems. In this work a new parameter  will be presented as a convex combination between RMIL and MMWU. The suggestion method always produces a descent search direction at each iteration. Under Strong Wolfe Powell (SWP) line search conditions, the global convergence of the proposed method is established. The preliminary numerical comparisons with some others CG methods have shown that this new method is efficient and robust in solving all given problems.

scholarly journals A new hybrid conjugate gradient algorithm for optimization models and its application to regression analysis

2021 ◽  
Vol 23 (2) ◽  
pp. 1100
Author(s):  
Ibrahim Mohammed Sulaiman ◽  
Norsuhaily Abu Bakar ◽  
Mustafa Mamat ◽  
Basim A. Hassan ◽  
Maulana Malik ◽  
...  
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Optimization Models ◽  
The Novel ◽  
Statistical Regression ◽  
Inexact Line Search ◽  
Sufficient Descent Condition ◽  
Unconstrained Optimization Problems

The hybrid conjugate gradient (CG) method is among the efficient variants of CG method for solving optimization problems. This is due to their low memory requirements and nice convergence properties. In this paper, we present an efficient hybrid CG method for solving unconstrained optimization models and show that the method satisfies the sufficient descent condition. The global convergence prove of the proposed method would be established under inexact line search. Application of the proposed method to the famous statistical regression model describing the global outbreak of the novel COVID-19 is presented. The study parameterized the model using the weekly increase/decrease of recorded cases from December 30, 2019 to March 30, 2020. Preliminary numerical results on some unconstrained optimization problems show that the proposed method is efficient and promising. Furthermore, the proposed method produced a good regression equation for COVID-19 confirmed cases globally.

scholarly journals A Three-Term Conjugate Gradient Algorithm with Quadratic Convergence for Unconstrained Optimization Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Gaoyi Wu ◽  
Yong Li ◽  
Gonglin Yuan
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Quadratic Convergence ◽  
Optimization Problems ◽  
Linear Convergence ◽  
Initial Step ◽  
Gradient Algorithm ◽  
Benchmark Problems ◽  
Unconstrained Optimization Problems

This paper further studies the WYL conjugate gradient (CG) formula with βkWYL≥0 and presents a three-term WYL CG algorithm, which has the sufficiently descent property without any conditions. The global convergence and the linear convergence are proved; moreover the n-step quadratic convergence with a restart strategy is established if the initial step length is appropriately chosen. Numerical experiments for large-scale problems including the normal unconstrained optimization problems and the engineer problems (Benchmark Problems) show that the new algorithm is competitive with the other similar CG algorithms.

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