A new spectral conjugate gradient method for large-scale unconstrained optimization

Jian, Jinbao; Qian, Chao; Jiang, Xianzhen; Zeng, Youfang; Yin, Jianghua

doi:10.1080/10556788.2016.1225213

Cited by 45 publications

(15 citation statements)

References 24 publications

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“…Obviously, the search direction d k generated by Algorithm 2 satisfies the sufficient descent condition (13). Therefore, if the stepsize α k is calculated by the Wolfe-Powell line search 1and 2, then the Zoutendijk condition (16) also holds for Algorithm 2.…”

Section: An Improved Version Of Lstt (Lstt+)mentioning

confidence: 99%

“…In recent years, based on the above classical formulas and line searches, many variations of CG methods have been proposed, including spectral CG methods [12,13], hybrid CG methods [14,15], and three-term CG methods [16,17]. Among them, the three-term CG methods seem to attract more attention, and a great deal of efforts has been devoted to developing this kind of methods, see, e.g., [18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

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Least-squares-based three-term conjugate gradient methods

Tang

Cui

2020

J Inequal Appl

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In this paper, we first propose a new three-term conjugate gradient (CG) method, which is based on the least-squares technique, to determine the CG parameter, named LSTT. And then, we present two improved variants of the LSTT CG method, aiming to obtain the global convergence property for general nonlinear functions. The least-squares technique used here well combines the advantages of two existing efficient CG methods. The search directions produced by the proposed three methods are sufficient descent directions independent of any line search procedure. Moreover, with the Wolfe-Powell line search, LSTT is proved to be globally convergent for uniformly convex functions, and the two improved variants are globally convergent for general nonlinear functions. Preliminary numerical results are reported to illustrate that our methods are efficient and have advantages over two famous three-term CG methods.

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Section: An Improved Version Of Lstt (Lstt+)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Least-squares-based three-term conjugate gradient methods

Tang

Cui

2020

J Inequal Appl

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“…Case (ii): For k ∈ I 2 , from (21) we have T k d k = − k 2 . By setting this equation and (5) in (25) imply that…”

Section: (H2)mentioning

confidence: 99%

Extended Dai-Yuan conjugate gradient strategy for large-scale unconstrained optimization with applications to compressive sensing

Esmaeili

Rostami

Kimiaei

2018

Filomat

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We present a new spectral conjugate gradient method based on the Dai-Yuan strategy to solve large-scale unconstrained optimization problems with applications to compressive sensing. In our method, the numerator of conjugate gradient parameter is a convex combination from the maximum gradient norm value in some preceding iterates and the current gradient norm value. This combination will try to produce the larger step-size far away from the optimizer and the smaller step-size close to it. In addition, the spectral parameter guarantees the descent property of the new generated direction in each iterate. The global convergence results are established under some standard assumptions. Numerical results are reported which indicate the promising behavior of the new procedure to solve large-scale unconstrained optimization and compressive sensing problems.

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“…Due to the strong convergence of the Newton method, Andrei [1] proposed an accelerated conjugate gradient method, which took advantage of the Newton method to improve the performance of the conjugate gradient method. Following this idea, Parvaneh et al [24] proposed a new SCG, which is a modified version of the method suggested by Jian et al [15]. Masoud [21] introduced a scaled conjugate gradient method which inherited the good properties of the classical conjugate gradient.…”

Section: Introductionmentioning

confidence: 99%

The new spectral conjugate gradient method for large-scale unconstrained optimisation

et al. 2020

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The spectral conjugate gradient methods are very interesting and have been proved to be effective for strictly convex quadratic minimisation. In this paper, a new spectral conjugate gradient method is proposed to solve large-scale unconstrained optimisation problems. Motivated by the advantages of approximate optimal stepsize strategy used in the gradient method, we design a new scheme for the choices of the spectral and conjugate parameters. Furthermore, the new search direction satisfies the spectral property and sufficient descent condition. Under some suitable assumptions, the global convergence of the developed method is established. Numerical comparisons show better behaviour of the proposed method with respect to some existing methods for a set of 130 test problems.

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A new spectral conjugate gradient method for large-scale unconstrained optimization

Cited by 45 publications

References 24 publications

Least-squares-based three-term conjugate gradient methods

Least-squares-based three-term conjugate gradient methods

Extended Dai-Yuan conjugate gradient strategy for large-scale unconstrained optimization with applications to compressive sensing

The new spectral conjugate gradient method for large-scale unconstrained optimisation

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