A Nonlinear Conjugate Gradient Algorithm with an Optimal Property and an Improved Wolfe Line Search

Dai, Yu‐Hong; Kou, Caixia

doi:10.1137/100813026

Cited by 258 publications

(135 citation statements)

References 36 publications

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“…Here, we present some numerical results obtained by applying C++ implementations of four versions of a CG method with the parameter (2.11) in which t is computed by (2.12) with ρ k = 1, guaranteing the sufficient descent property (1.10) and being an extended form of (1.9) which is an effective choice as stated in [11]. The methods are abbreviated by For the parameter r of the EDL and ZZ methods, we adopted the suggestion of [37] and set r = 1, when ||g k || ≥ 1, and r = 3, otherwise.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…yields another CG parameter suggested by Dai and Kou ( [11]). The choices (1.8) and (1.9) are effective since they guarantee the sufficient descent condition, i.e.,…”

Section: Introductionmentioning

confidence: 95%

“…where ̺ is a positive constant, independent of the line search and the objective function convexity, and lead to numerically efficient CG methods ( [4,11,19] [22]) and suggested a modified DL method which is globally convergent without convexity assumption on the objective function.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An extended Dai-Liao conjugate gradient method with global convergence for nonconvex functions

Arazm¹,

Babaie-Kafaki²,

Ghanbari³

2017

Glas. Mat. Ser. III

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Abstract. Using an extension of some previously proposed modified secant equations in the Dai-Liao approach, a modified nonlinear conjugate gradient method is proposed. As interesting features, the method employs the objective function values in addition to the gradient information and satisfies the sufficient descent property with proper choices for its parameter. Global convergence of the method is established without convexity assumption on the objective function. Results of numerical comparisons are reported. They demonstrate efficiency of the proposed method in the sense of the Dolan-Moré performance profile.

show abstract

Section: Numerical Experimentsmentioning

confidence: 99%

“…yields another CG parameter suggested by Dai and Kou ( [11]). The choices (1.8) and (1.9) are effective since they guarantee the sufficient descent condition, i.e.,…”

Section: Introductionmentioning

confidence: 95%

See 1 more Smart Citation

An extended Dai-Liao conjugate gradient method with global convergence for nonconvex functions

Arazm¹,

Babaie-Kafaki²,

Ghanbari³

2017

Glas. Mat. Ser. III

View full text Add to dashboard Cite

show abstract

“…Furthermore, Dai and Kou 13 used the spectral technique to analyse the CGD method, and suggested that the CGD method with t = 1 is better than that with t = 2.…”

Section: Algorithmmentioning

confidence: 99%

A derivative-free projection method for solving convex constrained monotone equations

Yuan¹

2017

ScienceAsia

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ABSTRACT:The CG_DESCENT (CGD) method is one of the most efficient conjugate gradient methods for solving unconstrained optimization problems. However, its applications in some other scenarios are relatively few. In this paper, inspired by one spectral PRP projection method, we extend the CGD method, and establish a derivative-free spectral CGD type projection method to solve large-scale nonlinear monotone equations with convex constraints. Due to it inheriting some nice properties of the conjugate gradient method such as the low memory requirement, the proposed method is very suitable to solve large-scale nonlinear monotone equations. Under appropriate conditions, we prove that the proposed method is globally convergent. Preliminary numerical results show that the proposed method works well.

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“…The first term in the right side of Eq. (3) is the data (4) which can be quickly evaluated using a conjugate gradient algorithm [16].…”

Section: Theorymentioning

confidence: 99%

High spatiotemporal resolution fMRI using partial separability model

Shi

Xie

Zhang

et al. 2015

BME

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Abstract. Blood oxygenation level dependent functional MRI (BOLD fMRI) requires repeatedly scanning the same region to capture neuronal activities, so the sampling data is very sparse along the temporal direction, which offers an opportunity to accelerate the fMRI. In this paper, (k-t) space data is sparsely acquired and reconstructed for BOLD fMRI using a partial separability (PS) model with a 2 " -norm constraint. The proposed approach achieves a high temporal resolution of 200 ms without compromising spatial resolution (3.5 u 3.5 u 4.0 mm 3 ). A simulation based on the EPI data with the right finger tapping experiment demonstrates that the proposed method can realize high spatiotemporal fMRI with accurate reconstruction of the activation regions from highly undersampled data. Meanwhile, preliminary in vivo experiment results also demonstrate the potential application of the proposed method in fMRI.

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A Nonlinear Conjugate Gradient Algorithm with an Optimal Property and an Improved Wolfe Line Search

Cited by 258 publications

References 36 publications

An extended Dai-Liao conjugate gradient method with global convergence for nonconvex functions

An extended Dai-Liao conjugate gradient method with global convergence for nonconvex functions

A derivative-free projection method for solving convex constrained monotone equations

High spatiotemporal resolution fMRI using partial separability model

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