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Projective Approximation Based Gradient Descent Modification. / Senov, Alexander; Granichin, Oleg.

In: IFAC-PapersOnLine, Vol. 50, No. 1, 2017, p. 3899-3904.

Research output: Contribution to journal › Article › peer-review

Harvard

Senov, A & Granichin, O 2017, 'Projective Approximation Based Gradient Descent Modification', IFAC-PapersOnLine, vol. 50, no. 1, pp. 3899-3904. https://doi.org/10.1016/j.ifacol.2017.08.362

APA

Senov, A., & Granichin, O. (2017). Projective Approximation Based Gradient Descent Modification. IFAC-PapersOnLine, 50(1), 3899-3904. https://doi.org/10.1016/j.ifacol.2017.08.362

Vancouver

Senov A, Granichin O. Projective Approximation Based Gradient Descent Modification. IFAC-PapersOnLine. 2017;50(1):3899-3904. https://doi.org/10.1016/j.ifacol.2017.08.362

Author

Senov, Alexander ; Granichin, Oleg. / Projective Approximation Based Gradient Descent Modification. In: IFAC-PapersOnLine. 2017 ; Vol. 50, No. 1. pp. 3899-3904.

BibTeX

@article{fa31db9d7ada4ea19cb99c179e25b2d1,
title = "Projective Approximation Based Gradient Descent Modification",
abstract = "We present a new modification of the gradient descent algorithm based on the surrogate optimization with projection into low-dimensional space. It iteratively approximates the target function in low-dimensional space and takes the approximation optimum point mapped back to original parameter space as next parameter estimate. Main contribution of the proposed method is in application of projection idea in approximation process. Major advantage of the proposed modification is that it does not change the gradient descent iterations, thus it can be used with some other variants of the gradient descent. We give a theoretical motivation for the proposed algorithm and a theoretical lower bound for its accuracy. Finally, we experimentally study its properties on modelled data.",
keywords = "Mathematical programming, Parameter estimation, Steepest descent, Least-squares, Function approximation, Convex optimization, Model approximation, Iterative methods, Quadratic programming, Projective methods, OPTIMIZATION, ALGORITHMS",
author = "Alexander Senov and Oleg Granichin",
year = "2017",
doi = "10.1016/j.ifacol.2017.08.362",
language = "Английский",
volume = "50",
pages = "3899--3904",
journal = "IFAC-PapersOnLine",
issn = "2405-8971",
publisher = "Elsevier",
number = "1",
note = "null ; Conference date: 09-07-2017 Through 14-07-2017",

}

RIS

TY - JOUR

T1 - Projective Approximation Based Gradient Descent Modification

AU - Senov, Alexander

AU - Granichin, Oleg

N1 - Conference code: 20

PY - 2017

Y1 - 2017

N2 - We present a new modification of the gradient descent algorithm based on the surrogate optimization with projection into low-dimensional space. It iteratively approximates the target function in low-dimensional space and takes the approximation optimum point mapped back to original parameter space as next parameter estimate. Main contribution of the proposed method is in application of projection idea in approximation process. Major advantage of the proposed modification is that it does not change the gradient descent iterations, thus it can be used with some other variants of the gradient descent. We give a theoretical motivation for the proposed algorithm and a theoretical lower bound for its accuracy. Finally, we experimentally study its properties on modelled data.

AB - We present a new modification of the gradient descent algorithm based on the surrogate optimization with projection into low-dimensional space. It iteratively approximates the target function in low-dimensional space and takes the approximation optimum point mapped back to original parameter space as next parameter estimate. Main contribution of the proposed method is in application of projection idea in approximation process. Major advantage of the proposed modification is that it does not change the gradient descent iterations, thus it can be used with some other variants of the gradient descent. We give a theoretical motivation for the proposed algorithm and a theoretical lower bound for its accuracy. Finally, we experimentally study its properties on modelled data.

KW - Mathematical programming

KW - Parameter estimation

KW - Steepest descent

KW - Least-squares

KW - Function approximation

KW - Convex optimization

KW - Model approximation

KW - Iterative methods

KW - Quadratic programming

KW - Projective methods

KW - OPTIMIZATION

KW - ALGORITHMS

UR - http://www.scopus.com/inward/record.url?scp=85031810902&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2017.08.362

DO - 10.1016/j.ifacol.2017.08.362

M3 - статья

AN - SCOPUS:85031810902

VL - 50

SP - 3899

EP - 3904

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8971

IS - 1

Y2 - 9 July 2017 through 14 July 2017

ER -

ID: 11874339