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Complete solution of a constrained tropical optimization problem with application to location analysis. / Кривулин, Николай Кимович.

Relational and Algebraic Methods in Computer Science: RAMICS 2014. ред. / Peter Höfner; Peter Jipsen; Wolfram Kahl; Martin Eric Müller. Cham : Springer Nature, 2014. стр. 362-378 (Lecture Notes in Computer Science; Том 8428).

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Harvard

Кривулин, НК 2014, Complete solution of a constrained tropical optimization problem with application to location analysis. в P Höfner, P Jipsen, W Kahl & ME Müller (ред.), Relational and Algebraic Methods in Computer Science: RAMICS 2014. Lecture Notes in Computer Science, Том. 8428, Springer Nature, Cham, стр. 362-378. https://doi.org/10.1007/978-3-319-06251-8_22

APA

Кривулин, Н. К. (2014). Complete solution of a constrained tropical optimization problem with application to location analysis. в P. Höfner, P. Jipsen, W. Kahl, & M. E. Müller (Ред.), Relational and Algebraic Methods in Computer Science: RAMICS 2014 (стр. 362-378). (Lecture Notes in Computer Science; Том 8428). Springer Nature. https://doi.org/10.1007/978-3-319-06251-8_22

Vancouver

Кривулин НК. Complete solution of a constrained tropical optimization problem with application to location analysis. в Höfner P, Jipsen P, Kahl W, Müller ME, Редакторы, Relational and Algebraic Methods in Computer Science: RAMICS 2014. Cham: Springer Nature. 2014. стр. 362-378. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-319-06251-8_22

Author

Кривулин, Николай Кимович. / Complete solution of a constrained tropical optimization problem with application to location analysis. Relational and Algebraic Methods in Computer Science: RAMICS 2014. Редактор / Peter Höfner ; Peter Jipsen ; Wolfram Kahl ; Martin Eric Müller. Cham : Springer Nature, 2014. стр. 362-378 (Lecture Notes in Computer Science).

BibTeX

@inbook{a284cc9fd8d74bc68319d6e99f2aba85,
title = "Complete solution of a constrained tropical optimization problem with application to location analysis",
abstract = "We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means of a conjugate transposition operator, subject to constraints in the form of linear vector inequalities. A complete direct solution to the problem under fairly general assumptions is given in a compact vector form suitable for both further analysis and practical implementation. We apply the result to solve a multidimensional minimax single facility location problem with Chebyshev distance and with inequality constraints imposed on the feasible location area.",
keywords = "idempotent semifield, tropical mathematics, minimax optimization problem, single facility location problem, Chebyshev distance",
author = "Кривулин, {Николай Кимович}",
year = "2014",
doi = "10.1007/978-3-319-06251-8_22",
language = "English",
isbn = "978-3-319-06250-1",
series = "Lecture Notes in Computer Science",
publisher = "Springer Nature",
pages = "362--378",
editor = "Peter H{\"o}fner and Peter Jipsen and Wolfram Kahl and M{\"u}ller, {Martin Eric}",
booktitle = "Relational and Algebraic Methods in Computer Science",
address = "Germany",

}

RIS

TY - CHAP

T1 - Complete solution of a constrained tropical optimization problem with application to location analysis

AU - Кривулин, Николай Кимович

PY - 2014

Y1 - 2014

N2 - We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means of a conjugate transposition operator, subject to constraints in the form of linear vector inequalities. A complete direct solution to the problem under fairly general assumptions is given in a compact vector form suitable for both further analysis and practical implementation. We apply the result to solve a multidimensional minimax single facility location problem with Chebyshev distance and with inequality constraints imposed on the feasible location area.

AB - We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means of a conjugate transposition operator, subject to constraints in the form of linear vector inequalities. A complete direct solution to the problem under fairly general assumptions is given in a compact vector form suitable for both further analysis and practical implementation. We apply the result to solve a multidimensional minimax single facility location problem with Chebyshev distance and with inequality constraints imposed on the feasible location area.

KW - idempotent semifield

KW - tropical mathematics

KW - minimax optimization problem

KW - single facility location problem

KW - Chebyshev distance

UR - https://arxiv.org/abs/1311.2795

U2 - 10.1007/978-3-319-06251-8_22

DO - 10.1007/978-3-319-06251-8_22

M3 - Chapter

SN - 978-3-319-06250-1

T3 - Lecture Notes in Computer Science

SP - 362

EP - 378

BT - Relational and Algebraic Methods in Computer Science

A2 - Höfner, Peter

A2 - Jipsen, Peter

A2 - Kahl, Wolfram

A2 - Müller, Martin Eric

PB - Springer Nature

CY - Cham

ER -

ID: 32917026