Tropical optimization problems

Николай Кимович Кривулин

Tropical optimization problems

Кафедра статистического моделирования

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › научная › рецензирование

Аннотация

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.

Язык оригинала	английский
Название основной публикации	Advances in Economics and Optimization
Подзаголовок основной публикации	Collected Scientific Studies Dedicated to the Memory of L. V. Kantorovich
Редакторы	Leon A. Petrosyan, Joseph V. Romanovsky, David W.-K. Yeung
Место публикации	New York
Издатель	Nova Science Publishers, Inc.
Страницы	195-214
ISBN (электронное издание)	978-1-63117-904-4
ISBN (печатное издание)	978-1-63117-073-7
Состояние	Опубликовано - 2014

Серия публикаций

Название	Economic Issues, Problems and Perspectives

Предметные области Scopus

Теория оптимизации
Теория управления и исследование операций
Алгебра и теория чисел

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1 выступление с устной презентацией

Об экстремальных задачах в тропической математике
Николай Кимович Кривулин (Докладчик)
8 фев 2012
Деятельность: выступление › выступление с устной презентацией
Международная конференция "Математика, экономика, менеджмент: 100 лет со дня рождения Л. В. Канторовича"
Николай Кимович Кривулин (Участник)
7 фев 2012 → 12 фев 2012
Деятельность: Участие в мероприятиях или организация мероприятий (событий) › Участие в конференции, заседании рабочей группы, ...

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

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author = "Кривулин, {Николай Кимович}",

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Tropical optimization problems. / Кривулин, Николай Кимович.

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

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › научная › рецензирование

TY - CHAP

T1 - Tropical optimization problems

AU - Кривулин, Николай Кимович

PY - 2014

Y1 - 2014

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 - https://novapublishers.com/shop/advances-in-economics-and-optimization-collected-scientific-studies-dedicated-to-the-memory-of-l-v-kantorovich/

UR - https://arxiv.org/abs/1408.0313

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T3 - Economic Issues, Problems and Perspectives

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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 -

Tropical optimization problems

Аннотация

Серия публикаций

Предметные области Scopus

Об экстремальных задачах в тропической математике

Международная конференция "Математика, экономика, менеджмент: 100 лет со дня рождения Л. В. Канторовича"

Цитировать