A tropical extremal problem with nonlinear objective function and linear inequality constraints
arXiv:1212.6106
Abstract
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.
The 6th WSEAS European Computing Conference (ECC'12), Prague, Czech Republic, September 24-26, 2012; Advances in Computer Science: Proc. 6th WSEAS European Computing Conf. (ECC '12), WSEAS Press. ISBN 978-1-61804-126-5; RACES 5, ISSN 1790-5109