A new conjugate gradient method with sufficient descent without any line search for unconstrained optimization

2015 ◽  
Author(s):  
Osman Omer ◽  
Mohd Rivaie ◽  
Mustafa Mamat ◽  
Zahrahtul Amani
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Sufficient Descent

scholarly journals A Conjugate Gradient Method for Unconstrained Optimization Problems

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Gonglin Yuan
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Sufficient Descent ◽  
Search Rule ◽  
Better Than

A hybrid method combining the FR conjugate gradient method and the WYL conjugate gradient method is proposed for unconstrained optimization problems. The presented method possesses the sufficient descent property under the strong Wolfe-Powell (SWP) line search rule relaxing the parameterσ<1. Under the suitable conditions, the global convergence with the SWP line search rule and the weak Wolfe-Powell (WWP) line search rule is established for nonconvex function. Numerical results show that this method is better than the FR method and the WYL method.

scholarly journals A New Modified Three-Term Hestenes–Stiefel Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Bakhtawar Baluch ◽  
Zabidin Salleh ◽  
Ahmad Alhawarat
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Sufficient Descent Property ◽  
Descent Property ◽  
Sufficient Descent

This paper describes a modified three-term Hestenes–Stiefel (HS) method. The original HS method is the earliest conjugate gradient method. Although the HS method achieves global convergence using an exact line search, this is not guaranteed in the case of an inexact line search. In addition, the HS method does not usually satisfy the descent property. Our modified three-term conjugate gradient method possesses a sufficient descent property regardless of the type of line search and guarantees global convergence using the inexact Wolfe–Powell line search. The numerical efficiency of the modified three-term HS method is checked using 75 standard test functions. It is known that three-term conjugate gradient methods are numerically more efficient than two-term conjugate gradient methods. Importantly, this paper quantifies how much better the three-term performance is compared with two-term methods. Thus, in the numerical results, we compare our new modification with an efficient two-term conjugate gradient method. We also compare our modification with a state-of-the-art three-term HS method. Finally, we conclude that our proposed modification is globally convergent and numerically efficient.

scholarly journals A NEW HYBRID PRP-MMSIS CONJUGATE GRADIENT METHOD AND ITS APPLICATION IN PORTOFOLIO SELECTION

2021 ◽  
Vol 5 (1) ◽  
pp. 47
Author(s):  
Sindy Devila ◽  
Maulana Malik ◽  
Wed Giyarti
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
New Method ◽  
Convergence Properties ◽  
Sufficient Descent Condition ◽  
Exact Line Search ◽  
Sufficient Descent ◽  
Descent Condition

In this paper, we propose a new hybrid coefficient of conjugate gradient method (CG) for solving unconstrained optimization model.  The new coefficient is combination of part the MMSIS (Malik et.al, 2020) and PRP (Polak, Ribi'ere \& Polyak, 1969) coefficients.  Under exact line search, the search direction of new method satisfies the sufficient descent condition and based on certain assumption, we establish the global convergence properties.  Using some test functions, numerical results show that the proposed method is more efficient than MMSIS method.  Besides, the new method can be used to solve problem in minimizing portfolio selection risk .

scholarly journals A modified quadratic hybridization of Polak-Ribiere-Polyak and Fletcher-Reeves conjugate gradient method for unconstrained optimization problems

2017 ◽  
Vol 7 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Pro Kaelo ◽  
Sindhu Narayanan ◽  
M.V. Thuto
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Hybrid Conjugate Gradient Method

This article presents a modified quadratic hybridization of the Polak–Ribiere–Polyak and Fletcher–Reeves conjugate gradient method for solving unconstrained optimization problems. Global convergence, with the strong Wolfe line search conditions, of the proposed quadratic hybrid conjugate gradient method is established. We also report some numerical results to show the competitiveness of the new hybrid method.

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