Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › Рецензирование
A constrained tropical optimization problem: complete solution and application example. / Кривулин, Николай Кимович.
Tropical and Idempotent Mathematics and Applications: International Workshop on Tropical and Idempotent Mathematics, August 26–31, 2012, Independent University, Moscow, Russia. ред. / G. L. Litvinov; S. N. Sergeev. Providence, Rhode Island : American Mathematical Society, 2014. стр. 163-177 (Contemporary Mathematics; Том 616).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › Рецензирование
}
TY - CHAP
T1 - A constrained tropical optimization problem: complete solution and application example
AU - Кривулин, Николай Кимович
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
UR - https://arxiv.org/abs/1305.1454
U2 - 10.1090/conm/616/12308
DO - 10.1090/conm/616/12308
M3 - Chapter
SN - 978-0-8218-9496-5
T3 - Contemporary Mathematics
SP - 163
EP - 177
BT - Tropical and Idempotent Mathematics and Applications
A2 - Litvinov, G. L.
A2 - Sergeev, S. N.
PB - American Mathematical Society
CY - Providence, Rhode Island
ER -
ID: 32916101