A Conjugate Gradient Method without Line Search and the Convergence Analysis

Huang, Jinhong; Zhou, Genjiao

doi:10.1109/eidwt.2013.133

Cited by 3 publications

(1 citation statement)

References 5 publications

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“…[17] introduced the conjugate gradient method (CGM), which was later expanded to include nonlinear CGM. To name a few, [2,4,6,9,11,14,15,18,20,32,33] have done extensive work on nonlinear CGM. Nonlinear CGMs are a good choice for effectively tackling (1), particularly when the dimension n is huge, for engineers and mathematicians because of the uncompoundedness of their analysis, their exceptionally high memory requirement, fast convergence, and excellent numerical execution in [8,20,21,29].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Conjugate Gradient Methods for Unconstrained Test Functions through an Approximate Wolfe Line Search

Adam,

Abdullahi,

Taiye

et al. 2024

CaJoST

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The nonlinear conjugate gradient method stands out as a potent iterative approach for tackling unconstrained large-scale optimization problems. A crucial aspect of any conjugate gradient algorithm lies in determining an optimal step length, a task for which various strategies have been put forth. To assess and contrast the performance of the approximate Wolfe line search technique, we conducted a numerical test across nine variants of nonlinear conjugate gradient methods. Through our experiments, a notable finding emerged: the Dai-Yuan nonlinear conjugate gradient method demonstrated a swifter convergence compared to its counterparts. The utilization of the approximate Wolfe line search technique, coupled with the distinctive features of the Dai-Yuan variant, contributed to its enhanced efficiency in navigating the optimization landscape. This empirical exploration sheds light on the nuanced dynamics within nonlinear conjugate gradient methods and underscores the significance of the selected strategy for approximating the Wolfe line search. The observed faster convergence of the Dai-Yuan method not only validates its efficacy but also suggests its potential applicability in scenarios where rapid and effective optimization is paramount.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Conjugate Gradient Methods for Unconstrained Test Functions through an Approximate Wolfe Line Search

Adam,

Abdullahi,

Taiye

et al. 2024

CaJoST

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A Fast Cyclic Spectrum Detection Algorithm for MWC Based on Lorentzian Norm

Peng

Han

Sun

2018

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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A Step-Length Formula for Conjugate Gradient Methods

Ishaq

Latunde

Akande³

2020

MJoC

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A new step-length formula is proposed for the conjugate gradient methods. The unified formula for obtaining step-length does not involve any matrix operation. Numerical results obtained are graphically illustrated using performance profiling software. This showed that the new formula performs efficiently in terms of computational efforts and execution time compared with some existing formulae for obtaining the step-length without line search procedures.

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A Conjugate Gradient Method without Line Search and the Convergence Analysis

Cited by 3 publications

References 5 publications

Nonlinear Conjugate Gradient Methods for Unconstrained Test Functions through an Approximate Wolfe Line Search

Nonlinear Conjugate Gradient Methods for Unconstrained Test Functions through an Approximate Wolfe Line Search

A Fast Cyclic Spectrum Detection Algorithm for MWC Based on Lorentzian Norm

A Step-Length Formula for Conjugate Gradient Methods

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