Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization

Sim, Hong Seng; Leong, Wah June; Chen, Chuei Yee; Ibrahim, Siti Nur Iqmal

doi:10.3934/naco.2018024

Cited by 2 publications

(2 citation statements)

References 5 publications

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“…Also, it is important to state spectral gradient method. Therein the updating of the formula for B k+1 is done in the following way [111]…”

Section: 1mentioning

confidence: 99%

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A survey of gradient methods for solving nonlinear optimization

Stanimirović¹,

Mathematics²,

Ivanov³

et al. 2020

era

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<p style='text-indent:20px;'>The paper surveys, classifies and investigates theoretically and numerically main classes of line search methods for unconstrained optimization. Quasi-Newton (QN) and conjugate gradient (CG) methods are considered as representative classes of effective numerical methods for solving large-scale unconstrained optimization problems. In this paper, we investigate, classify and compare main QN and CG methods to present a global overview of scientific advances in this field. Some of the most recent trends in this field are presented. A number of numerical experiments is performed with the aim to give an experimental and natural answer regarding the numerical one another comparison of different QN and CG methods.</p>

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“…Also, it is important to state spectral gradient method. Therein the updating of the formula for B k+1 is done in the following way [111]…”

Section: 1mentioning

confidence: 99%

“…A modification of the quasi-Newton method in defining the two-phase approximate greatest descent was used in [71]. Several variants of multistep spectral gradient methods for solving large scale unconstrained optimization problems were proposed in [111]. Usage of an optimization algorithm in artificial neural networks was considered in [75].…”

mentioning

confidence: 99%

A survey of gradient methods for solving nonlinear optimization

Stanimirović¹,

Mathematics²,

Ivanov³

et al. 2020

era

View full text Add to dashboard Cite

show abstract

Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization

Sim

Chen

Leong

et al. 2022

JIMO

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<p style='text-indent:20px;'>This paper proposes a nonmonotone spectral gradient method for solving large-scale unconstrained optimization problems. The spectral parameter is derived from the eigenvalues of an optimally sized memoryless symmetric rank-one matrix obtained under the measure defined as a ratio of the determinant of updating matrix over its largest eigenvalue. Coupled with a nonmonotone line search strategy where backtracking-type line search is applied selectively, the spectral parameter acts as a stepsize during iterations when no line search is performed and as a milder form of quasi-Newton update when backtracking line search is employed. Convergence properties of the proposed method are established for uniformly convex functions. Extensive numerical experiments are conducted and the results indicate that our proposed spectral gradient method outperforms some standard conjugate-gradient methods.</p>

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Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization

Cited by 2 publications

References 5 publications

A survey of gradient methods for solving nonlinear optimization

A survey of gradient methods for solving nonlinear optimization

Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization

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