A Nonmonotone Modified BFGS Method for Non-Convex Minimization

2014 ◽  
Vol 556-562 ◽  
pp. 4023-4026
Author(s):  
Ting Feng Li ◽  
Zhi Yuan Liu ◽  
Sheng Hui Yan
Keyword(s):  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Convergence Property ◽  
Bfgs Method ◽  
Remarkable Feature ◽  
Convexity Assumption ◽  
Unconstrained Optimization Problems ◽  
Global Convergence Property ◽  
Large Scale Unconstrained Optimization

In this paper, a modification BFGS method with nonmonotone line-search for solving large-scale unconstrained optimization problems is proposed. A remarkable feature of the proposed method is that it possesses a global convergence property even without convexity assumption on the objective function. Some numerical results are reported which illustrate that the proposed method is efficient

A Modified Limited Memory BFGS Method for Non-Convex Minimization

2014 ◽  
Vol 530-531 ◽  
pp. 367-371
Author(s):  
Ting Feng Li ◽  
Yu Ting Zhang ◽  
Sheng Hui Yan
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Test Problems ◽  
Bfgs Method ◽  
Remarkable Feature ◽  
Limited Memory Bfgs Method ◽  
Limited Memory ◽  
Unconstrained Optimization Problems ◽  
Global Convergence Property ◽  
Large Scale Unconstrained Optimization

In this paper, a modified limited memory BFGS method for solving large-scale unconstrained optimization problems is proposed. A remarkable feature of the proposed method is that it possesses a global convergence property even without convexity assumption on the objective function. The implementations of the algorithm on CUTE test problems are reported, which suggest that a slight improvement has been achieved.

scholarly journals An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Ahmad Alhawarat ◽  
Thoi Trung Nguyen ◽  
Ramadan Sabra ◽  
Zabidin Salleh
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Unconstrained Optimization Problem ◽  
Descent Property ◽  
Large Scale Unconstrained Optimization

To find a solution of unconstrained optimization problems, we normally use a conjugate gradient (CG) method since it does not cost memory or storage of second derivative like Newton’s method or Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. Recently, a new modification of Polak and Ribiere method was proposed with new restart condition to give a so-call AZPRP method. In this paper, we propose a new modification of AZPRP CG method to solve large-scale unconstrained optimization problems based on a modification of restart condition. The new parameter satisfies the descent property and the global convergence analysis with the strong Wolfe-Powell line search. The numerical results prove that the new CG method is strongly aggressive compared with CG_Descent method. The comparisons are made under a set of more than 140 standard functions from the CUTEst library. The comparison includes number of iterations and CPU time.

scholarly journals Solving a large scale nonlinear unconstrained optimization problems by using new coefficient of conjugate gradient method with exact line search direction

2018 ◽  
Vol 7 (3.28) ◽  
pp. 92
Author(s):  
Talat Alkouli ◽  
Mustafa Mamat ◽  
Mohd Rivaie ◽  
Puspa Liza Ghazali
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Large Scale Unconstrained Optimization

In this paper, an efficient modification of nonlinear conjugate gradient method and an associated implementation, based on an exact line search, are proposed and analyzed to solve large-scale unconstrained optimization problems. The method satisfies the sufficient descent property. Furthermore, global convergence result is proved. Computational results for a set of unconstrained optimization test problems, some of them from CUTE library, showed that this new conjugate gradient algorithm seems to converge more stable and outperforms the other similar methods in many situations.   

scholarly journals New scaled algorithm for non-linear conjugate gradients in unconstrained optimization

2021 ◽  
Vol 24 (3) ◽  
pp. 1589
Author(s):  
Ghada M. Al-Naemi ◽  
Ahmed H. Sheekoo
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Numerical Experiments ◽  
Large Scale ◽  
Line Search ◽  
Convergence Property ◽  
Line Searches ◽  
Descent Property ◽  
Global Convergence Property ◽  
Large Scale Unconstrained Optimization

<p>A new scaled conjugate gradient (SCG) method is proposed throughout this paper, the SCG technique may be a special important generalization conjugate gradient (CG) method, and it is an efficient numerical method for solving nonlinear large scale unconstrained optimization. As a result, we proposed the new SCG method with a strong Wolfe condition (SWC) line search is proposed. The proposed technique's descent property, as well as its global convergence property, are satisfied without the use of any line searches under some suitable assumptions. The proposed technique's efficiency and feasibility are backed up by numerical experiments comparing them to traditional CG techniques.</p>

A modified conjugate gradient coefficient under exact line search for unconstrained optimization

2018 ◽  
Vol 7 (3.28) ◽  
pp. 84 ◽  
Author(s):  
Nurul Aini ◽  
Nurul Hajar ◽  
Mohd Rivaie ◽  
Mustafa Mamat
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Mild Conditions ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Numerical Performance ◽  
Large Scale Unconstrained Optimization

The conjugate gradient (CG) method is a well-known solver for large-scale unconstrained optimization problems. In this paper, a modified CG method based on AMR* and CD method is presented. The resulting algorithm for the new CG method is proved to be globally convergent under exact line search both under some mild conditions. Comparisons of numerical performance are made involving the new method and four other CG methods. The results show that the proposed method is more efficient.  

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 An Extension of Polak-Ribière-Polyak Method using Exact Line Search

2019 ◽  
Vol 8 (2S3) ◽  
pp. 368-373
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Test Problems ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent ◽  
Large Scale Unconstrained Optimization

Lately, many large-scale unconstrained optimization problems rely upon nonlinear conjugate gradient (CG) methods. Many areas such as engineering, and computer science have benefited because of its simplicity, fast and low memory requirements. Many modified coefficients have appeared recently, all of which to improve these methods. This paper considers an extension conjugate gradient method of PolakRibière-Polyak using exact line search to show that it holds for some properties such as sufficient descent and global convergence. A set of 113 test problems is used to evaluate the performance of the proposed method and get compared to other existing methods using the same line search.

scholarly journals Global Convergence of a New Coefficient Nonlinear Conjugate Gradient Method

2018 ◽  
Vol 11 (3) ◽  
pp. 1188
Author(s):  
Nur Syarafina Mohamed ◽  
Mustafa Mamat ◽  
Mohd Rivaie ◽  
Shazlyn Milleana Shaharuddin
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Search Direction ◽  
Nonlinear Conjugate Gradient Method ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Conjugate Gradient ◽  
Large Scale Unconstrained Optimization

Nonlinear conjugate gradient (CG) methods are widely used in optimization field due to its efficiency for solving a large scale unconstrained optimization problems. Many studies and modifications have been developed in order to improve the method. The method is known to possess sufficient descend condition and its global convergence properties under strong Wolfe-Powell search direction. In this paper, the new coefficient of CG method is presented. The global convergence and sufficient descend properties of the new coefficient are established by using strong Wolfe-Powell line search direction. Results show that the new coefficient is able to globally converge under certain assumptions and theories.

scholarly journals A modifications of conjugate gradient method for unconstrained optimization problems

2018 ◽  
Vol 7 (2.14) ◽  
pp. 21
Author(s):  
Omar Alshorman ◽  
Mustafa Mamat ◽  
Ahmad Alhawarat ◽  
Mohd Revaie
Keyword(s):  
Global Convergence ◽  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Convergence Properties ◽  
Unconstrained Optimization Problems ◽  
Large Scale Unconstrained Optimization

The Conjugate Gradient (CG) methods play an important role in solving large-scale unconstrained optimization problems. Several studies have been recently devoted to improving and modifying these methods in relation to efficiency and robustness. In this paper, a new parameter of CG method has been proposed. The new parameter possesses global convergence properties under the Strong Wolfe-Powell (SWP) line search. The numerical results show that the proposed formula is more efficient and robust compared with Polak-Rribiere Ployak (PRP), Fletcher-Reeves (FR) and Wei, Yao, and Liu (WYL) parameters.  

scholarly journals On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Min Sun ◽  
Jing Liu
Keyword(s):  
Strong Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Line Searches ◽  
Unconstrained Optimization Problems ◽  
Sufficient Descent ◽  
Large Scale Unconstrained Optimization

Recently, Zhang et al. proposed a sufficient descent Polak-Ribière-Polyak (SDPRP) conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense thatlim infk→∞∥∇f(xk)∥=0when an Armijo-type line search is used. In this paper, motivated by the line searches proposed by Shi et al. and Zhang et al., we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense thatlimk→∞∥∇f(xk)∥=0under the two new line searches. Numerical results are reported to show the efficiency of the SDPRP with the new Armijo-type line searches in practical computation.

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