An Adaptive Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition

2019 ◽  
Author(s):  
Xiao-Liang Dong ◽  
Zhi-Feng Dai ◽  
Reza Ghanbari ◽  
Xiang-Li Li
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Conjugacy Condition ◽  
Sufficient Descent Condition ◽  
Sufficient Descent ◽  
Descent Condition

scholarly journals A NEW THREE–TERM CONJUGATE GRADIENT METHOD WITH DESCENT DIRECTION FOR UNCONSTRAINED OPTIMIZATION

2016 ◽  
Vol 21 (3) ◽  
pp. 399-411 ◽  
Author(s):  
XiaoLiang Dong ◽  
HongWei Liu ◽  
YuBo He ◽  
Saman Babaie-Kafaki ◽  
Reza Ghanbari
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Numerical Comparison ◽  
Conjugacy Condition ◽  
Sufficient Descent Condition ◽  
Line Searches ◽  
Sufficient Descent ◽  
Descent Condition

In this paper, we propose a three–term PRP–type conjugate gradient method which always satisfies the sufficient descent condition independently of line searches employed. An important property of our method is that its direction is closest to the direction of the Newton method or satisfies conjugacy condition as the iterations evolve. In addition, under mild condition, we prove global convergence properties of the proposed method. Numerical comparison illustrates that our proposed method is efficient for solving the optimization problems.

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.

scholarly journals A New conjugate gradient method for unconstrained optimization problems with descent property

2020 ◽  
Vol 9 (2) ◽  
pp. 101-105
Author(s):  
Hussein Ageel Khatab ◽  
Salah Gazi Shareef
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Conjugacy Condition ◽  
Sufficient Descent Condition ◽  
Unconstrained Optimization Problems ◽  
Descent Condition ◽  
Nonlinear Unconstrained Optimization

In this paper, we propose a new conjugate gradient method for solving nonlinear unconstrained optimization. The new method consists of three parts, the first part of them is the parameter of Hestenes-Stiefel (HS). The proposed method is satisfying the descent condition, sufficient descent condition and conjugacy condition. We give some numerical results to show the efficiency of the suggested method.

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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