Extremal properties of tropical eigenvalues and solutions to tropical optimization problems

Standard

Extremal properties of tropical eigenvalues and solutions to tropical optimization problems. / Krivulin, N.

In: Linear Algebra and Its Applications, Vol. 468, 2015, p. 211-232.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{4742b4d233294f718f4b879f10757954,

title = "Extremal properties of tropical eigenvalues and solutions to tropical optimization problems",

abstract = "An unconstrained optimization problem is formulated in terms of tropical mathematics to minimize a functional that is defined on a vector set by a matrix and calculated through multiplicative conjugate transposition. For some particular cases, the minimum in the problem is known to be equal to the tropical spectral radius of the matrix. We examine the problem in the common setting of a general idempotent semifield. A complete direct solution in a compact vector form is obtained to this problem under fairly general conditions. The result is extended to solve new tropical optimization problems with more general objective functions and inequality constraints. Applications to real-world problems that arise in project scheduling are presented. To illustrate the results obtained, numerical examples are also provided.",

keywords = "Idempotent semifield, Eigenvalue, Linear inequality, Optimization problem, Direct solution, Project scheduling",

author = "N. Krivulin",

year = "2015",

doi = "10.1016/j.laa.2014.06.044",

language = "English",

volume = "468",

pages = "211--232",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Extremal properties of tropical eigenvalues and solutions to tropical optimization problems

AU - Krivulin, N.

PY - 2015

Y1 - 2015

N2 - An unconstrained optimization problem is formulated in terms of tropical mathematics to minimize a functional that is defined on a vector set by a matrix and calculated through multiplicative conjugate transposition. For some particular cases, the minimum in the problem is known to be equal to the tropical spectral radius of the matrix. We examine the problem in the common setting of a general idempotent semifield. A complete direct solution in a compact vector form is obtained to this problem under fairly general conditions. The result is extended to solve new tropical optimization problems with more general objective functions and inequality constraints. Applications to real-world problems that arise in project scheduling are presented. To illustrate the results obtained, numerical examples are also provided.

AB - An unconstrained optimization problem is formulated in terms of tropical mathematics to minimize a functional that is defined on a vector set by a matrix and calculated through multiplicative conjugate transposition. For some particular cases, the minimum in the problem is known to be equal to the tropical spectral radius of the matrix. We examine the problem in the common setting of a general idempotent semifield. A complete direct solution in a compact vector form is obtained to this problem under fairly general conditions. The result is extended to solve new tropical optimization problems with more general objective functions and inequality constraints. Applications to real-world problems that arise in project scheduling are presented. To illustrate the results obtained, numerical examples are also provided.

KW - Idempotent semifield

KW - Eigenvalue

KW - Linear inequality

KW - Optimization problem

KW - Direct solution

KW - Project scheduling

UR - https://arxiv.org/abs/1311.0442

U2 - 10.1016/j.laa.2014.06.044

DO - 10.1016/j.laa.2014.06.044

M3 - Article

VL - 468

SP - 211

EP - 232

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

ID: 3923211