A New Modification of NPRP Conjugate Gradient Method for Unconstrained Optimization

Malik, Maulana; Mamat, Mustafa; Abas, Siti Sabariah; Sulaiman, Ibrahim Mohammed

doi:10.37418/amsj.9.7.61

Cited by 9 publications

(11 citation statements)

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“…We begin this section by showing that the new parameter satisfies the sufficient descent property. From [7], it follows that KMAR parameter will reduce to the following:…”

Section: Convergence Resultsmentioning

confidence: 99%

“…where f is a smooth function defined by f : R n → R whose gradient g(x) = ∇f (x) is always available [1]. Problem in the form (1) can be found in various specialized disciplines such as computer science, machine learning, neural network, engineering, statistics and many more (see [2][3][4][5][6][7]). For simplicity, the following abbreviations ∇(f (x k )) and f (x k ) would be represented by ∇ k and f k throughout this study and denote the Euclidean norm of vectors.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Performance evaluation of a novel Conjugate Gradient Method for training feed forward neural network

Kamilu¹,

Sulaiman²,

Muhammad³

et al. 2023

Math. Model. Comput.

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In this paper, we construct a new conjugate gradient method for solving unconstrained optimization problems. The proposed method satisfies the sufficient decent property irrespective of the line search and the global convergence was established under some suitable. Further, the new method was used to train different sets of data via a feed forward neural network. Results obtained show that the proposed algorithm significantly reduces the computational time by speeding up the directional minimization with a faster convergence rate.

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“…We begin this section by showing that the new parameter satisfies the sufficient descent property. From [7], it follows that KMAR parameter will reduce to the following:…”

Section: Convergence Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Performance evaluation of a novel Conjugate Gradient Method for training feed forward neural network

Kamilu¹,

Sulaiman²,

Muhammad³

et al. 2023

Math. Model. Comput.

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show abstract

“…Property (*) Consider a CG algorithm generated using algorithm 1. Assume for all 𝑘 ≥ 0, we have 0 < 𝛾 ≤ ‖𝑔 𝑘 ‖ ≤ 𝛾 , (27) for some positive constants 𝛾 and 𝛾. Then, we say the method possesses the property (*), if…”

Section: Proofmentioning

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

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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.

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“…The CG algorithms are unconstrained optimization processes characterized by their simplicity, nice convergence properties, low memory requirements, and less computational cost in the iteration process (Malik et al, 2020). For more details on hybrid conjugate methods, refer to (Touati-Ahmed and Storey, 1990;Gilbert and Nocedal, 1992;Dai and Yuan, 2001;Andrei, 2008;Liu and Li, 2014;Yakubu et al, 2020;Malik et al, 2021;Sulaiman and Mamat, 2020a;Sulaiman et al, 2022a). This paper defines a new hybrid CG algorithm using an inexact line search procedure to solve intuitionistic fuzzy nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Hybrid Conjugate Gradient Algorithm for Solving Intuitionistic Fuzzy Nonlinear Equations

Omesa¹,

Sulaiman²,

Yusuf³

et al. 2023

BAS-SJKFU

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This paper presents an iterative algorithm for solving intuitionistic fuzzy nonlinear equations (IFNEs). The proposed method is based on the classical conjugate gradient (CG) search direction. An interesting feature of the new algorithm is that it considers problems based on the special triangular intuitionistic fuzzy number. For this purpose, intuitionistic fuzzy quantities are transformed into membership and non-membership parametric forms, and a line search procedure is employed to compute the step length. Preliminary results from numerical experiments are presented to demonstrate the performance of the method. It is observed that the proposed hybrid CG method is highly effective and promising. KEYWORDS Hybrid CG, intuitionistic fuzzy nonlinear equation, parametric form, step length, inexact line search

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A New Modification of NPRP Conjugate Gradient Method for Unconstrained Optimization

Cited by 9 publications

References 0 publications

Performance evaluation of a novel Conjugate Gradient Method for training feed forward neural network

Performance evaluation of a novel Conjugate Gradient Method for training feed forward neural network

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

An Efficient Hybrid Conjugate Gradient Algorithm for Solving Intuitionistic Fuzzy Nonlinear Equations

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