A constrained tropical optimization problem: complete solution and application example

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийглава/разделнаучнаярецензирование

Аннотация

This paper focuses on a multidimensional optimization problem, which is formulated in terms of tropical mathematics and consists in minimizing a nonlinear objective function subject to linear inequality constraints. To solve the problem, we follow an approach based on the introduction of an additional unknown variable to reduce the problem to solving linear inequalities, where the variable plays the role of a parameter. A necessary and sufficient condition for the inequalities to hold is used to evaluate the parameter, whereas the general solution of the inequalities is taken as a solution of the original problem. Under fairly general assumptions, a complete direct solution to the problem is obtained in a compact vector form. The result is applied to solve a problem in project scheduling when an optimal schedule is given by minimizing the flow time of activities in a project under various activity precedence constraints. As an illustration, a numerical example of optimal scheduling is also presented.
Язык оригиналаанглийский
Название основной публикацииTropical and Idempotent Mathematics and Applications
Подзаголовок основной публикацииInternational Workshop on Tropical and Idempotent Mathematics, August 26–31, 2012, Independent University, Moscow, Russia
РедакторыG. L. Litvinov, S. N. Sergeev
Место публикацииProvidence, Rhode Island
ИздательAmerican Mathematical Society
Страницы163-177
ISBN (печатное издание)978-0-8218-9496-5
DOI
СостояниеОпубликовано - 2014

Серия публикаций

НазваниеContemporary Mathematics
ИздательAmerican Mathematical Society
Том616
ISSN (печатное издание)0271-4132
ISSN (электронное издание)1098-3627

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Предметные области Scopus

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

Цитировать

Кривулин, Н. К. (2014). A constrained tropical optimization problem: complete solution and application example. В G. L. Litvinov, & S. N. Sergeev (Ред.), Tropical and Idempotent Mathematics and Applications: International Workshop on Tropical and Idempotent Mathematics, August 26–31, 2012, Independent University, Moscow, Russia (стр. 163-177). (Contemporary Mathematics; Том 616). Providence, Rhode Island: American Mathematical Society. https://doi.org/10.1090/conm/616/12308