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Method of Steepest Descent for Two-Dimensional Problems of Calculus of Variations. / Dolgopolik, M.V.; Tamasyan, G.Sh.

Constructive Nonsmooth Analysis and Related Topics (Springer Optimization and Its Applications, Volume 87). Springer Nature, 2014. p. 253 стр., 101-113.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Harvard

Dolgopolik, MV & Tamasyan, GS 2014, Method of Steepest Descent for Two-Dimensional Problems of Calculus of Variations. in Constructive Nonsmooth Analysis and Related Topics (Springer Optimization and Its Applications, Volume 87). Springer Nature, pp. 253 стр., 101-113. https://doi.org/10.1007/978-1-4614-8615-2_7

APA

Dolgopolik, M. V., & Tamasyan, G. S. (2014). Method of Steepest Descent for Two-Dimensional Problems of Calculus of Variations. In Constructive Nonsmooth Analysis and Related Topics (Springer Optimization and Its Applications, Volume 87) (pp. 253 стр., 101-113). Springer Nature. https://doi.org/10.1007/978-1-4614-8615-2_7

Vancouver

Dolgopolik MV, Tamasyan GS. Method of Steepest Descent for Two-Dimensional Problems of Calculus of Variations. In Constructive Nonsmooth Analysis and Related Topics (Springer Optimization and Its Applications, Volume 87). Springer Nature. 2014. p. 253 стр., 101-113 https://doi.org/10.1007/978-1-4614-8615-2_7

Author

Dolgopolik, M.V. ; Tamasyan, G.Sh. / Method of Steepest Descent for Two-Dimensional Problems of Calculus of Variations. Constructive Nonsmooth Analysis and Related Topics (Springer Optimization and Its Applications, Volume 87). Springer Nature, 2014. pp. 253 стр., 101-113

BibTeX

@inbook{ca142a4dd543408a878cac8e68c20c86,
title = "Method of Steepest Descent for Two-Dimensional Problems of Calculus of Variations",
abstract = "In this paper we demonstrate an application of nonsmooth analysis and the theory of exact penalty functions to two-dimensional problems of the calculus of variations. We derive necessary conditions for an extremum in the problem under consideration and use them to construct a new direct numerical minimization method (the method of steepest descent). We prove the convergence of the method and give numerical examples that show the efficiency of the suggested method.The described method can be very useful for solving various practical problems of mechanics, mathematical physics and calculus of variations.",
keywords = "Method of steepest descent, Two-dimensional problem, Calculus of variations",
author = "M.V. Dolgopolik and G.Sh. Tamasyan",
year = "2014",
doi = "10.1007/978-1-4614-8615-2_7",
language = "English",
isbn = "978-1-4614-8614-5",
pages = "253 стр., 101--113",
booktitle = "Constructive Nonsmooth Analysis and Related Topics (Springer Optimization and Its Applications, Volume 87)",
publisher = "Springer Nature",
address = "Germany",

}

RIS

TY - CHAP

T1 - Method of Steepest Descent for Two-Dimensional Problems of Calculus of Variations

AU - Dolgopolik, M.V.

AU - Tamasyan, G.Sh.

PY - 2014

Y1 - 2014

N2 - In this paper we demonstrate an application of nonsmooth analysis and the theory of exact penalty functions to two-dimensional problems of the calculus of variations. We derive necessary conditions for an extremum in the problem under consideration and use them to construct a new direct numerical minimization method (the method of steepest descent). We prove the convergence of the method and give numerical examples that show the efficiency of the suggested method.The described method can be very useful for solving various practical problems of mechanics, mathematical physics and calculus of variations.

AB - In this paper we demonstrate an application of nonsmooth analysis and the theory of exact penalty functions to two-dimensional problems of the calculus of variations. We derive necessary conditions for an extremum in the problem under consideration and use them to construct a new direct numerical minimization method (the method of steepest descent). We prove the convergence of the method and give numerical examples that show the efficiency of the suggested method.The described method can be very useful for solving various practical problems of mechanics, mathematical physics and calculus of variations.

KW - Method of steepest descent

KW - Two-dimensional problem

KW - Calculus of variations

U2 - 10.1007/978-1-4614-8615-2_7

DO - 10.1007/978-1-4614-8615-2_7

M3 - Chapter

SN - 978-1-4614-8614-5

SP - 253 стр., 101-113

BT - Constructive Nonsmooth Analysis and Related Topics (Springer Optimization and Its Applications, Volume 87)

PB - Springer Nature

ER -

ID: 4645320