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Tropical optimization problems. / Krivulin, Nikolai K.

Advances in Economics and Optimization: Collected Scientific Studies Dedicated to the Memory of L. V. Kantorovich. ed. / Leon A. Petrosyan; Joseph V. Romanovsky; David W.-K. Yeung. New York : Nova Science Publishers, Inc., 2014. p. 195-214 (Economic Issues, Problems and Perspectives).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Krivulin, NK 2014, Tropical optimization problems. in LA Petrosyan, JV Romanovsky & DW-K Yeung (eds), Advances in Economics and Optimization: Collected Scientific Studies Dedicated to the Memory of L. V. Kantorovich. Economic Issues, Problems and Perspectives, Nova Science Publishers, Inc., New York, pp. 195-214. <https://arxiv.org/abs/1408.0313>

APA

Krivulin, N. K. (2014). Tropical optimization problems. In L. A. Petrosyan, J. V. Romanovsky, & D. W-K. Yeung (Eds.), Advances in Economics and Optimization: Collected Scientific Studies Dedicated to the Memory of L. V. Kantorovich (pp. 195-214). (Economic Issues, Problems and Perspectives). Nova Science Publishers, Inc.. https://arxiv.org/abs/1408.0313

Vancouver

Krivulin NK. Tropical optimization problems. In Petrosyan LA, Romanovsky JV, Yeung DW-K, editors, Advances in Economics and Optimization: Collected Scientific Studies Dedicated to the Memory of L. V. Kantorovich. New York: Nova Science Publishers, Inc. 2014. p. 195-214. (Economic Issues, Problems and Perspectives).

Author

Krivulin, Nikolai K. / Tropical optimization problems. Advances in Economics and Optimization: Collected Scientific Studies Dedicated to the Memory of L. V. Kantorovich. editor / Leon A. Petrosyan ; Joseph V. Romanovsky ; David W.-K. Yeung. New York : Nova Science Publishers, Inc., 2014. pp. 195-214 (Economic Issues, Problems and Perspectives).

BibTeX

@inbook{1c02b6698b214b0fb2de15f14c2e8024,

title = "Tropical optimization problems",

abstract = "We consider optimization problems that are formulated and solved in the framework of tropical mathematics. The problems consist in minimizing or maximizing functionals defined on vectors of finite-dimensional semimodules over idempotent semifields, and may involve constraints in the form of linear equations and inequalities. The objective function can be either a linear function or nonlinear function calculated by means of multiplicative conjugate transposition of vectors. We start with an overview of known tropical optimization problems and solution methods. Then, we formulate certain new problems and present direct solutions to the problems in a closed compact vector form suitable for further analysis and applications. For many problems, the results obtained are complete solutions.",

keywords = "idempotent semifield, tropical optimization, nonlinear objective function, linear constraints, Chebyshev approximation",

author = "Krivulin, {Nikolai K.}",

year = "2014",

month = apr,

day = "1",

language = "English",

isbn = "978-1-63117-073-7",

series = "Economic Issues, Problems and Perspectives",

publisher = "Nova Science Publishers, Inc.",

pages = "195--214",

editor = "Petrosyan, {Leon A.} and Romanovsky, {Joseph V.} and Yeung, {David W.-K.}",

booktitle = "Advances in Economics and Optimization",

address = "United States",

}

RIS

TY - CHAP

T1 - Tropical optimization problems

AU - Krivulin, Nikolai K.

PY - 2014/4/1

Y1 - 2014/4/1

N2 - We consider optimization problems that are formulated and solved in the framework of tropical mathematics. The problems consist in minimizing or maximizing functionals defined on vectors of finite-dimensional semimodules over idempotent semifields, and may involve constraints in the form of linear equations and inequalities. The objective function can be either a linear function or nonlinear function calculated by means of multiplicative conjugate transposition of vectors. We start with an overview of known tropical optimization problems and solution methods. Then, we formulate certain new problems and present direct solutions to the problems in a closed compact vector form suitable for further analysis and applications. For many problems, the results obtained are complete solutions.

AB - We consider optimization problems that are formulated and solved in the framework of tropical mathematics. The problems consist in minimizing or maximizing functionals defined on vectors of finite-dimensional semimodules over idempotent semifields, and may involve constraints in the form of linear equations and inequalities. The objective function can be either a linear function or nonlinear function calculated by means of multiplicative conjugate transposition of vectors. We start with an overview of known tropical optimization problems and solution methods. Then, we formulate certain new problems and present direct solutions to the problems in a closed compact vector form suitable for further analysis and applications. For many problems, the results obtained are complete solutions.

KW - idempotent semifield

KW - tropical optimization

KW - nonlinear objective function

KW - linear constraints

KW - Chebyshev approximation

UR - http://www.scopus.com/inward/record.url?scp=84956760986&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:84956760986

SN - 978-1-63117-073-7

T3 - Economic Issues, Problems and Perspectives

SP - 195

EP - 214

BT - Advances in Economics and Optimization

A2 - Petrosyan, Leon A.

A2 - Romanovsky, Joseph V.

A2 - Yeung, David W.-K.

PB - Nova Science Publishers, Inc.

CY - New York

ER -

ID: 9182783