A conjugate gradient method with inexact line search for unconstrained optimization

Hamoda, Mohamed; Rivaie, Mohd; Mamat, Mustafa; Salleh, Zabidin

doi:10.12988/ams.2015.411995

Cited by 5 publications

(3 citation statements)

References 19 publications

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“…Two novel CGMs were proposed based on the new conjugacy requirement, one of which was found to be particularly efficient. A modified PRP CG approach was introduced by Mohammed et al (2015) to solve large-scale unconstrained optimization problems where the parameter is restricted and the sufficient descent property is satisfied under the strong Wolfe-Powell line search. Zhang (2009) introduced two new variants of Hestenes-Stiefel nonlinear CGM, based on the secant condition commonly met by quasi-Newton methods, which are descent methods even with inexact line searches.…”

Section: Review Of Related Literaturesmentioning

confidence: 99%

Integration of Modified Classical Conjugate Gradient Methods for Unconstrained Optimization

B. Onuoha

2024

AJBAR

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The integration of modified classical conjugate gradient methods (CGMs) for unconstrained optimization represents a crucial and evolving area of research within the field of optimization algorithms. Over time, numerous studies have put forth diverse modifications and novel approaches to enhance the effectiveness of classical CGMs. These modifications aim to address specific challenges and improve the overall performance of optimization algorithms in unconstrained scenarios. In order to tackle unconstrained optimization challenges and improve our understanding of their synergies, this ongoing study aims to unify different modified classical CGMs. Conventional CGMs have proven effective for optimization tasks, and a range of different approaches have been produced by carefully modifying these techniques. The main goal of this paper is to combine these modified versions, with particular attention to those that have similar numerators. The integration process involves systematically merging the advantageous aspects of these modified methods to develop not only innovative but also more resilient approaches to unconstrained optimization problems. The ultimate goal of this unification effort is to capitalize on the strengths inherent in different approaches to create a cohesive framework that significantly improves overall optimization performance. To thoroughly assess the efficacy of the integrated methods, a series of comprehensive performance tests are conducted. These tests include a meticulous comparison of outcomes with those of classical CGMs, providing valuable insights into the relative strengths and weaknesses of the modified approaches across diverse optimization scenarios. The evaluation criteria encompass convergence rates, solution accuracy, and computational efficiency. The conclusive outcome demonstrates that the unified approaches consistently outperform individual methods across all three crucial evaluation criteria.

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Section: Review Of Related Literaturesmentioning

confidence: 99%

Integration of Modified Classical Conjugate Gradient Methods for Unconstrained Optimization

B. Onuoha

2024

AJBAR

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“…In this study, a new CG method with namely UAM k  (Ummie, Asrul and Mustafa) proposed by pursuing the excellent performance of coefficient proposed by [22], [7] in term of successful to solve the test problem. x  based on (2) 6.…”

Section: A Propose New Coefficientmentioning

confidence: 99%

New Conjugate Gradient Method Addressing Large Scale Unconstrained Optimization Problem

2019

IJITEE

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An iterative conjugate gradient (CG) method is prominently known for dealing with unconstrained optimization problem. A new CG method which is modified by Wei Yao Liu (WYL) method is tested by standard test functions. Moreover, the step size is calculated using exact line search. Theoretical proofs on convergence analysis are shown. As a result, this new CG is comparable to the other methods in finding the optimal points by measuring the total iterations required as well as the computing time. Numerical results showed the execution between three CG methods in details.

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“…During the last decade, much effort has been devoted to developing new modifications of conjugate gradient methods which do not only possess strong convergence properties, but they are also computationally superior to the classical methods. Such methods can be found in [18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Section: New Formula For K  and Its Propertiesmentioning

confidence: 99%

A conjugate gradient method with strong Wolfe-Powell line search for unconstrained optimization

Hamoda¹,

Mamat²,

Rivaie³

et al. 2016

ams

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In this paper, a modified conjugate gradient method is presented for solving large-scale unconstrained optimization problems, which possesses the sufficient descent property with Strong Wolfe-Powell line search. A global convergence result was proved when the (SWP) line search was used under some conditions. Computational results for a set consisting of 138 unconstrained optimization test problems showed that this new conjugate gradient algorithm seems to converge more stable and is superior to other similar methods in many situations.

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A conjugate gradient method with inexact line search for unconstrained optimization

Cited by 5 publications

References 19 publications

Integration of Modified Classical Conjugate Gradient Methods for Unconstrained Optimization

Integration of Modified Classical Conjugate Gradient Methods for Unconstrained Optimization

New Conjugate Gradient Method Addressing Large Scale Unconstrained Optimization Problem

A conjugate gradient method with strong Wolfe-Powell line search for unconstrained optimization

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