Application of spectral conjugate gradient methods for solving unconstrained optimization problems

Sulaiman, Ibrahim Mohammed; Yakubu, Usman Abbas; Mamat, Mustafa

doi:10.11121/ijocta.01.2020.00859

Cited by 21 publications

(7 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We considered 𝜀 = 10 (= the gradient value as the stopping criteria as Hillstrom, and Kenneth [24] suggested that ‖𝑔 " ‖ ≤ 𝜀 . This stopping criterion has also been used in several current literatures such as by Ibrahim et al, [25] and Sulaiman et al, [26] and to the latest by Ishak et al, [27]. For each test function, we used initial point that is a closer point to the solution for every problem.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Pre-Numerical Tests for a New Conjugate Gradient Method

Rahma Mohamed,

Shalela Mohd Mahali,

Noor Ilyani Izzati

et al. 2024

ARASET

View full text Add to dashboard Cite

The performance of a new beta in conjugate gradient method is generally measured on its CPU time and the number of iterations using large scale problems without concerning the accuracy of the solution attained. The method is claimed to be the best when less CPU time is used in comparison with the other classical beta. However, the accuracy of the solution gained compared to the exact solution of the function has never been tested as part of the performance measurement. Our previous research has already proven that our new beta perform well in both speed and number of iterations used. Therefore, in this research, we will accommodate this with alternative numerical test on the new beta in assessing the accuracy of the gained solution. This is to further ensure the efficiency of the new beta. Assessment was done with four other classical conjugate gradient methods on fourteen small scale problems. Results attained were promising to be tested for more tests in real functional problems.

show abstract

Section: Numerical Results and Discussionmentioning

confidence: 99%

Pre-Numerical Tests for a New Conjugate Gradient Method

Rahma Mohamed,

Shalela Mohd Mahali,

Noor Ilyani Izzati

et al. 2024

ARASET

View full text Add to dashboard Cite

show abstract

“…In a constrained optimization problem with bounded condition, there is a spectral parameter with memoryless property for Broydon class presented by Nakayama et al 13 . Eventually, for a real live example, scientist use the spectral algorithms to analyze the problems as a drug abuse problems; see 14 .…”

Section: Now Consider a Minimization Of Unconstrained Problemmentioning

confidence: 99%

Modifications for Quasi-Newton Method and Its Spectral Algorithm for Solving Unconstrained Optimization Problems

Sadraddin,

Latif

2024

Baghdad Sci.J

View full text Add to dashboard Cite

In this paper, two modifications for spectral quasi-Newton algorithm of type BFGS are imposed. In the first algorithm, named SQNEI, a certain spectral parameter is used in such a step for BFGS algorithm differs from other presented algorithms. The second algorithm, SQNEv-Iv, has both new parameter position and value suggestion. In SQNEI and SQNEv-Iv methods, the parameters are involved in a search direction after an approximated Hessian matrix is updated. It is provided that two methods are effective under some assumptions. Moreover, the sufficient descent property is proved as well as the global and superlinear convergence for SQNEv-Iv and SQNEI. Both of them are superior the standard BFGS (QNBFGS) and previous spectral quasi-Newton (SQNLC). However, SQNEv-Iv is outstanding SQNEI if it is convergent to the solution. This means that, two modified methods are in the race for the more efficiency method in terms less iteration numbers and consuming time in running CPU. Finally, numerical results are presented for the four algorithms by running list of test problems with inexact line search satisfying Armijo condition.

show abstract

“…The CG method is one of the popular iterative algorithms used to solve real life application problems because of their efficiency and good memory requirement [39]. Recently, researchers have investigated the performance of different CG formula on image restoration, Portfolio selection, regression model, signal recovery, and motion control of robotic trajectories [6,17,22,24,26,[39][40][41][42][43][44][45]. Therefore, in this study, we study the performance of the proposed CG method on problem for robotic motion control.…”

Section: Application To Robotic Motion Controlmentioning

confidence: 99%

“…However, the methods presented in (7) are influenced by jamming phenomena which affects their computational performance [16,21]. The convergence issues from the first set of CG methods defined in (6) and the poor numerical results from the second set (7) has led to numerous studies of the CG formulas [16,[22][23][24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

A Modified Wei-Yao-Liu Conjugate Gradient Method for Unconstrained Optimization and Motion Control of Robotic Motion Manipulators

Saleh Nazzal Alsuliman,

Nur Fadhilah Ibrahim,

Nur Aidya Hanum Aizam

2023

ARASET

View full text Add to dashboard Cite

The WYL-type conjugate gradient (CG) iterative formulas have been widely studied by researchers because of their effective and robust algorithms as well as less memory requirements. However, recent modifications of the WYL formulas are very complicated for unconstrained optimization. Also, the performance of most of these methods are yet to be verified on real-life application problems. In this study, a new modification of Wei-Yao-Liu (WYL) CG formula was presented to compute the search direction of robotic motion control and unconstrained optimization problems (UOP). This study discussed the general convergence results of the new formula under suitable assumptions and showed that the scheme possesses the descent properties under inexact line search. Numerical results on some set of robotic motion control and UOP show that the new formula outperformed some existing formulas with the same characteristics. The new method was able to solved 100% of the test problems while WYL was able to solve about 90% and the other methods solved less than 50% of the test problems respectively.

show abstract

Application of spectral conjugate gradient methods for solving unconstrained optimization problems

Cited by 21 publications

References 10 publications

Pre-Numerical Tests for a New Conjugate Gradient Method

Pre-Numerical Tests for a New Conjugate Gradient Method

Modifications for Quasi-Newton Method and Its Spectral Algorithm for Solving Unconstrained Optimization Problems

A Modified Wei-Yao-Liu Conjugate Gradient Method for Unconstrained Optimization and Motion Control of Robotic Motion Manipulators

Contact Info

Product

Resources

About