TY - CHAP

T1 - A tropical extremal problem with nonlinear objective function and linear inequality constraints

AU - Krivulin, Nikolai

PY - 2012

Y1 - 2012

N2 - We consider a multidimensional extremal problem formulated in terms of tropical mathematics. The problem is to minimize a nonlinear objective function, which is defined on a finite-dimensional semimodule over an idempotent semifield, subject to linear inequality constraints. An efficient solution approach is developed which reduces the problem to that of solving a linear inequality with an extended set of unknown variables. We use the approach to obtain a complete solution to the problem in a closed form under quite general assumptions. To illustrate the obtained results, a two-dimensional problem is examined and its numerical solution is given.

AB - We consider a multidimensional extremal problem formulated in terms of tropical mathematics. The problem is to minimize a nonlinear objective function, which is defined on a finite-dimensional semimodule over an idempotent semifield, subject to linear inequality constraints. An efficient solution approach is developed which reduces the problem to that of solving a linear inequality with an extended set of unknown variables. We use the approach to obtain a complete solution to the problem in a closed form under quite general assumptions. To illustrate the obtained results, a two-dimensional problem is examined and its numerical solution is given.

KW - Idempotent semifield

KW - Nonlinear functional

KW - Linear inequality

KW - Matrix trace

KW - Spectral radius

KW - Tropical extremal problem

KW - Closed-form solution

M3 - Chapter

SN - 978-1-61804-126-5

SP - 528 стр., 216-221

BT - Advances in Computer Science: Proc. 6th Europ. Computing Conf. (ECC'12), Prague, Czech Republic, September 24-26, 2012. Vol. 5 of Recent Advances in Computer Engineering Series.

PB - WSEAS - World Scientific and Engineering Academy and Society

ER -