A hybrid conjugate gradient method with descent property for unconstrained optimization

Jian, Jinbao; Han, Lin; Jiang, Xianzhen

doi:10.1016/j.apm.2014.08.008

Cited by 56 publications

(21 citation statements)

References 27 publications

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“…Since Problem (34) is a standard smooth optimization problem, many powerful optimization techniques can be directly applied to solve it (see [37][38][39][40]).…”

Section: Definitionmentioning

confidence: 99%

A New Smoothing Method for Mathematical Programs with Complementarity Constraints Based on Logarithm-Exponential Function

Wan

2018

Mathematical Problems in Engineering

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We present a new smoothing method based on a logarithm-exponential function for mathematical program with complementarity constraints (MPCC). Different from the existing smoothing methods available in the literature, we construct an approximate smooth problem of MPCC by partly smoothing the complementarity constraints. With this new method, it is proved that the Mangasarian-Fromovitz constraint qualification holds for the approximate smooth problem. Convergence of the approximate solution sequence, generated by solving a series of smooth perturbed subproblems, is investigated. Under the weaker constraint qualification MPCC-Cone-Continuity Property, it is proved that any accumulation point of the approximate solution sequence is a M-stationary point of the original MPCC. Preliminary numerical results indicate that the developed algorithm based on the partly smoothing method is efficient, particularly in comparison with the other similar ones.

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“…Since Problem (34) is a standard smooth optimization problem, many powerful optimization techniques can be directly applied to solve it (see [37][38][39][40]).…”

Section: Definitionmentioning

confidence: 99%

A New Smoothing Method for Mathematical Programs with Complementarity Constraints Based on Logarithm-Exponential Function

Wan

2018

Mathematical Problems in Engineering

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“…Quite recently, based on the ideas of hybrid methods, Jian et al [16] introduced a new hybrid choice for parameter β k as follows:…”

Section: Preliminariesmentioning

confidence: 99%

“…It is well-known that the FR method and the DY method usually possess nice convergence property but have poor numerical performance. On the contrary, the PRP method and the HS method are generally regarded to be two of the most efficient conjugate gradient methods, but their convergence properties are not so good [16]. To the best of our knowledge, many conjugate gradient type methods for (2) need the restart technique [7,17,18].…”

Section: Introductionmentioning

confidence: 98%

New hybrid conjugate gradient projection method for the convex constrained equations

Sun

Liu

2015

Calcolo

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Based on the two famous Hestenes-Stiefel and Dai-Yuan conjugate gradient methods, a new hybrid conjugate gradient projection method is proposed for the convex constrained equations. At each iteration, the new method is fully free from any derivative evaluations. Furthermore, the search direction generated by the proposed method satisfies the sufficient descent property, which is independent of the line search. Under the condition that the underlying mapping is continuous and monotone, we establish the global convergence of the new method. Compared with traditional methods for solving such problem, our new method does not require the Lipschitz continuity of the underlying mapping. Some large-scale numerical tests are performed and reported, which show that the proposed method is efficient and promising.

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“…Thus, to overcome these shortcomings of the classical CGMs, many researchers pay great attention to improve the CGMs. As a result, many improvements with excellent theoretical properties and numerical performance of the CGMs results were proposed, for example, References [7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Where, the spectral conjugate gradient method (SCGM) proposed by Birgin and Martinez [12] can be seen as an important development of CGM.…”

Section: Introductionmentioning

confidence: 99%

“…and fully absorbing the hybrid idea of Reference [11], we propose a new conjugate parameter in the following manner…”

Section: Introductionmentioning

confidence: 99%

A Spectral Conjugate Gradient Method with Descent Property

et al. 2020

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Spectral conjugate gradient method (SCGM) is an important generalization of the conjugate gradient method (CGM), and it is also one of the effective numerical methods for large-scale unconstrained optimization. The designing for the spectral parameter and the conjugate parameter in SCGM is a core work. And the aim of this paper is to propose a new and effective alternative method for these two parameters. First, motivated by the strong Wolfe line search requirement, we design a new spectral parameter. Second, we propose a hybrid conjugate parameter. Such a way for yielding the two parameters can ensure that the search directions always possess descent property without depending on any line search rule. As a result, a new SCGM with the standard Wolfe line search is proposed. Under usual assumptions, the global convergence of the proposed SCGM is proved. Finally, by testing 108 test instances from 2 to 1,000,000 dimensions in the CUTE library and other classic test collections, a large number of numerical experiments, comparing with both SCGMs and CGMs, for the presented SCGM are executed. The detail results and their corresponding performance profiles are reported, which show that the proposed SCGM is effective and promising.

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A hybrid conjugate gradient method with descent property for unconstrained optimization

Cited by 56 publications

References 27 publications

A New Smoothing Method for Mathematical Programs with Complementarity Constraints Based on Logarithm-Exponential Function

A New Smoothing Method for Mathematical Programs with Complementarity Constraints Based on Logarithm-Exponential Function

New hybrid conjugate gradient projection method for the convex constrained equations

A Spectral Conjugate Gradient Method with Descent Property

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