Tropical optimization problems

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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 оригиналаанглийский
Название основной публикацииAdvances in Economics and Optimization
Подзаголовок основной публикацииCollected Scientific Studies Dedicated to the Memory of L. V. Kantorovich
РедакторыLeon A. Petrosyan, Joseph V. Romanovsky, David W.-K. Yeung
Место публикацииNew York
ИздательNova Science Publishers, Inc.
Страницы195-214
ISBN (электронное издание)978-1-63117-904-4
ISBN (печатное издание)978-1-63117-073-7
СостояниеОпубликовано - 2014

Серия публикаций

НазваниеEconomic Issues, Problems and Perspectives

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Предметные области Scopus

  • Теория оптимизации
  • Теория управления и исследование операций
  • Алгебра и теория чисел

Цитировать

Кривулин, Н. К. (2014). Tropical optimization problems. В L. A. Petrosyan, J. V. Romanovsky, & D. W-K. Yeung (Ред.), Advances in Economics and Optimization: Collected Scientific Studies Dedicated to the Memory of L. V. Kantorovich (стр. 195-214). (Economic Issues, Problems and Perspectives). New York: Nova Science Publishers, Inc..