The Sufficient descent condition of the Polak–Ribière–Polyak (PRP) conjugate gradient method without line search

2021 ◽  
Author(s):  
Osman Yousif
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Sufficient Descent Condition ◽  
Sufficient Descent ◽  
Descent Condition

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 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.

Convergence of the descent Dai–Yuan conjugate gradient method for unconstrained optimization

2011 ◽  
Vol 18 (9) ◽  
pp. 1249-1253 ◽  
Author(s):  
Mehdi Dehghan ◽  
Masoud Hajarian
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Convergence Result ◽  
Sufficient Descent Condition ◽  
Exact Line Search ◽  
Sufficient Descent

The conjugate gradient method is one of the most useful and the earliest-discovered techniques for solving large-scale nonlinear optimization problems. Many variants of this method have been proposed, and some are widely used in practice. In this article, we study the descent Dai–Yuan conjugate gradient method which guarantees the sufficient descent condition for any line search. With exact line search, the introduced conjugate gradient method reduces to the Dai–Yuan conjugate gradient method. Finally, a global convergence result is established when the line search fulfils the Goldstein conditions.

scholarly journals Descent Condition for a Scalar Parameter of Spectral HS (SpHS) Conjugate Gradient Method

2019 ◽  
Vol 8 (4) ◽  
pp. 11464-11467
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Standard Test ◽  
Exact Line Search ◽  
Sufficient Descent ◽  
Descent Condition ◽  
Spectral Conjugate Gradient ◽  
Unconstrained Problems

Spectral conjugate gradient method has been used in most cases as an alternative to the conjugate gradient (CG) method in order to solve nonlinear unconstrained problems. In this paper, we introduced a spectral parameter of HS conjugate gradient method resultant from the classical CG search direction and used some of the standard test functions with numerous variables to prove its sufficient descent and global convergence properties, the numerical outcome is verified by exact line search procedures.

scholarly journals A New Conjugate Gradient Coefficient for Unconstrained Optimization Based On Dai-Liao

2019 ◽  
Vol 7 (1) ◽  
pp. 34-36
Author(s):  
Alaa L. Ibrahim ◽  
Muhammad A. Sadiq ◽  
Salah G. Shareef
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Numerical Results ◽  
Sufficient Descent Condition ◽  
Sufficient Descent ◽  
Descent Condition ◽  
Number Of Iterations

This paper, proposes a new conjugate gradient method for unconstrained optimization based on Dai-Liao (DL) formula; descent condition and sufficient descent condition for our method are provided. The numerical results and comparison show that the proposed algorithm is potentially efficient when we compare with (PR) depending on number of iterations (NOI) and the number of functions evaluation (NOF).

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