A Barzilai-Borwein conjugate gradient method

Dai, Yu‐Hong; Kou, Caixia

doi:10.1007/s11425-016-0279-2

Cited by 42 publications

(28 citation statements)

References 22 publications

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“…I to estimate B k , which had been proposed by Dai and Kou (2016). Under such condition, the condition number of B k will be also reasonable and…”

Section: The Search Directionmentioning

confidence: 91%

“…The relevant research of the SMCG method has attracted many scholars. Dai and Kou (2016) estimated the parameter in SMCG based on the analysis of Barzilai-Borwein (1988) idea and SMCG, and the corresponding method was called BBCG. Inspired by SMCG and BBCG, Liu and Liu (2019) presented an efficient Barzilai-Borwein conjugate gradient method with the generalized Wolfe line search.…”

Section: Introductionmentioning

confidence: 99%

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A new subspace minimization conjugate gradient method based on modified secant equation for unconstrained optimization

Diao

Liu

2020

Comp. Appl. Math.

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In this paper, a new subspace minimization conjugate gradient method based on modified secant equation is proposed and analyzed. For a classical subspace minimization conjugate gradient method, the search direction is derived by minimizing an approximate quadratic model of objective function in a two-dimensional subspace. Generally, the approximate Hessian matrix in the above quadratic model is required to satisfy the standard secant equation, while we consider an approximate Hessian matrix which satisfies the modified secant equation. We give some rules such that if these rules are satisfied, we choose the standard secant equation, otherwise we choose the modified one. We can prove that the proposed directions satisfy the sufficient descent property under some extra conditions. We also present a modified nonmonotone Wolfe line search and establish the global convergence of the proposed method for general nonlinear functions under mild assumptions. Numerical comparisons are given with famous CG_DESCENT (5.3) (Hager and Zhang in

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“…I to estimate B k , which had been proposed by Dai and Kou (2016). Under such condition, the condition number of B k will be also reasonable and…”

Section: The Search Directionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

A new subspace minimization conjugate gradient method based on modified secant equation for unconstrained optimization

Diao

Liu

2020

Comp. Appl. Math.

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“…It is not difficult to see that different values of ρ k+1 lead to different results of d k+1 , some choices of ρ k+1 have been suggested in Dai and Kou (2016), Yuan and Stoer (1995). In this paper, we present a new ρ k+1 to keep the A k+1 positive definite and to guarantee the d k+1 sufficient descent.…”

Section: Conic Modelmentioning

confidence: 99%

“…The classical conjugate gradient methods are only the special cases where the objective function is quadratic and line searches are exact. Based on the analysis of SMCG, Dai and Kou (2016) chose the parameter in the method by combining the Barzilai-Borwein idea (Barzilai and Borwein 1988), denoted by the BBCG method. Inspired by SMCG and BBCG, Liu and Liu (2018a) presented an efficient Barzilai-Borwein conjugate gradient method (SMCG_BB) with the generalized Wolfe line search for unconstrained optimization.…”

Section: Introductionmentioning

confidence: 99%

A subspace minimization conjugate gradient method based on conic model for unconstrained optimization

Liu

2019

Comp. Appl. Math.

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In this paper, we present a new conjugate gradient method, in which the search direction is computed by minimizing a selected approximate model in a two-dimensional subspace. That is, if the objective function is not close to a quadratic, the search direction is generated by a conic model. Otherwise, a quadratic model is considered. The direction of the proposed method is proved to possess the sufficient descent property. With the modified nonmonotone line search, we establish a global convergence of the proposed method under appropriate assumptions. R-linear convergence of the proposed method is also analyzed. Numerical results using two different test function collections show that the proposed algorithm is efficient.

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“…Masoud [21] introduced a scaled conjugate gradient method which inherited the good properties of the classical conjugate gradient. More references in this field can be seen in [6,10,20,28,34].…”

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 Barzilai-Borwein conjugate gradient method

Cited by 42 publications

References 22 publications

A new subspace minimization conjugate gradient method based on modified secant equation for unconstrained optimization

A new subspace minimization conjugate gradient method based on modified secant equation for unconstrained optimization

A subspace minimization conjugate gradient method based on conic model for unconstrained optimization

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

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