TY - GEN

T1 - Использование разрежения матриц для решения многомерной задачи тропической оптимизации

AU - Кривулин, Николай Кимович

AU - Сорокин, Владимир Николаевич

N1 - Кривулин Н. К., Сорокин В. Н. Использование разрежения матриц для решения многомерной задачи тропической оптимизации // International Scientific Conference, 13-16 December, 2017, Borovets, Bulgaria. Mathematical Modeling. Technological and Socio-Economic Processes. Proceedings. Sofia: Scientific-Technical Union of Mechanical Engineering “INDUSTRY 4.0”, 2017. P. 36-39.

PY - 2017

Y1 - 2017

N2 - A complete solution is proposed for a problem of vector-valued function minimization with elements from a tropical (idempotent) semifield. The tropical optimization problem, considered here, arises when one needs, for instance, to find the best, in the sense of Chebyshev metric, approximate solution for tropical vector equations, and occurs in various applications, including scheduling, location and decision-making problems. To solve the problem, first, the minimum value of the objective function is obtained, a characterization of the solution set in the form of a system of inequalities is proposed, and one of the solutions is presented. Then, with introduction of matrix sparsification into the problem, an extended set of solutions, and then a complete solution in the form of a family of subsets are derived. Procedures, allowing to reduce the number of subsets, which one needs to examine when constructing the complete solution, are described in the present paper. It is shown how the complete solution can be represented in parametric way in a compact vector form.

AB - A complete solution is proposed for a problem of vector-valued function minimization with elements from a tropical (idempotent) semifield. The tropical optimization problem, considered here, arises when one needs, for instance, to find the best, in the sense of Chebyshev metric, approximate solution for tropical vector equations, and occurs in various applications, including scheduling, location and decision-making problems. To solve the problem, first, the minimum value of the objective function is obtained, a characterization of the solution set in the form of a system of inequalities is proposed, and one of the solutions is presented. Then, with introduction of matrix sparsification into the problem, an extended set of solutions, and then a complete solution in the form of a family of subsets are derived. Procedures, allowing to reduce the number of subsets, which one needs to examine when constructing the complete solution, are described in the present paper. It is shown how the complete solution can be represented in parametric way in a compact vector form.

KW - idempotent semifield

KW - tropical optimization

KW - Chebyshev approximation

KW - complete solution

KW - matrix sparsification

UR - http://www.mathmodel.eu/sbornik/1-2017.pdf

M3 - статья в сборнике материалов конференции

VL - 1

T3 - International Scientific Conference. Mathematical Modeling

SP - 36

EP - 39

BT - International Scientific Conference, 13-16 December, 2017, Borovets, Bulgaria. Mathematical Modeling

PB - Scientific Technical Union of Mechanical Engineering «INDUSTRY 4.0»

CY - Sofia

T2 - International Scientific Conference “Mathematical Modeling”<br/>

Y2 - 13 December 2017 through 16 December 2017

ER -