Hybridization of accelerated gradient descent method

Petrović, Milena J.; Rakočević, Vladimir; Kontrec, Nataša; Panic, Stefan; Ilić, Dejan

doi:10.1007/s11075-017-0460-4

Cited by 30 publications

(43 citation statements)

References 19 publications

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“…Numerical tests from [3] confirmed that the hybrid model (16) upgrades its forerunner SM iterative rule.…”

Section: Preliminaries: Accelerated Gradient Methods and Hybrid Iteramentioning

confidence: 84%

“…A common way to determine this parameter is through the features of the second-order Taylor's series taken on appropriate scheme (6). Acceleration parameters that were computed in such way are applied in the methods described in [1][2][3][4][5]. According to the iteration form (6), we can conclude that the accelerated gradient methods are of the quasi-Newton type in which the approximation of the Hessian, i.e., its inverse, is obtained by the scalar matrix , where is appropriate identity matrix and = ( , −1 ) is the matching acceleration parameter.…”

Section: Preliminaries: Accelerated Gradient Methods and Hybrid Iteramentioning

confidence: 99%

“…(HSM method [3]). An interesting concept of merging iterations through the hybrid expression was suggested in some research articles (see [6][7][8]).…”

Section: Preliminaries: Accelerated Gradient Methods and Hybrid Iteramentioning

confidence: 99%

“…proposed by Picard, Mann, and Ishikawa, upgrades the hybrid models mentioned above. The authors of [3] used the advantages of the hybrid model (15) and derived a hybrid version of the accelerated gradient SM method from [1], termed the HSM method and defined by…”

Section: Preliminaries: Accelerated Gradient Methods and Hybrid Iteramentioning

confidence: 99%

See 3 more Smart Citations

Hybrid Modification of Accelerated Double Direction Method

Petrović¹,

Stanimirović

Kontrec³

et al. 2018

Mathematical Problems in Engineering

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We present a hybridization of the accelerated gradient method with two vector directions. This hybridization is based on the usage of a chosen three-term hybrid model. Derived hybrid accelerated double direction model keeps preferable properties of both included methods. Convergence analysis demonstrates at least linear convergence of the proposed iterative scheme on the set of uniformly convex and strictly convex quadratic functions. The results of numerical experiments confirm better performance profile in favor of derived hybrid accelerated double direction model when compared to its forerunners.

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“…Numerical tests from [3] confirmed that the hybrid model (16) upgrades its forerunner SM iterative rule.…”

Section: Preliminaries: Accelerated Gradient Methods and Hybrid Iteramentioning

confidence: 84%

Section: Preliminaries: Accelerated Gradient Methods and Hybrid Iteramentioning

confidence: 99%

“…(HSM method [3]). An interesting concept of merging iterations through the hybrid expression was suggested in some research articles (see [6][7][8]).…”

Section: Preliminaries: Accelerated Gradient Methods and Hybrid Iteramentioning

confidence: 99%

Section: Preliminaries: Accelerated Gradient Methods and Hybrid Iteramentioning

confidence: 99%

See 2 more Smart Citations

Hybrid Modification of Accelerated Double Direction Method

Petrović¹,

Stanimirović

Kontrec³

et al. 2018

Mathematical Problems in Engineering

Self Cite

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“…Finally, let us emphasize that contemporary papers often use the Picard-Mann-Ishikawa iterative processes and they make the connection of these kinds of processes with the unconstrained optimization (see [29,37,38]).…”

Section: Resultsmentioning

confidence: 99%

Unconstrained Optimization Methods: Conjugate Gradient Methods and Trust-Region Methods

Djordjević¹

2019

Applied Mathematics

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Here, we consider two important classes of unconstrained optimization methods: conjugate gradient methods and trust region methods. These two classes of methods are very interesting; it seems that they are never out of date. First, we consider conjugate gradient methods. We also illustrate the practical behavior of some conjugate gradient methods. Then, we study trust region methods. Considering these two classes of methods, we analyze some recent results.

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The data filtering based multiple‐stage Levenberg–Marquardt algorithm for Hammerstein nonlinear systems

Kang

Liu

2021

Intl J Robust & Nonlinear

117

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This article considers the parameter identification problem of multiple-input single-output Hammerstein nonlinear systems. Applying the data filtering technique, the input-output data are filtered. The filtered system is decomposed into multiple subsystems with fewer variables by using the hierarchical identification principle. The data filtering based multiple-stage Levenberg-Marquardt algorithm is proposed for interactively identifying each subsystem. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms.

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Hybridization of accelerated gradient descent method

Cited by 30 publications

References 19 publications

Hybrid Modification of Accelerated Double Direction Method

Hybrid Modification of Accelerated Double Direction Method

Unconstrained Optimization Methods: Conjugate Gradient Methods and Trust-Region Methods

The data filtering based multiple‐stage Levenberg–Marquardt algorithm for Hammerstein nonlinear systems

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