A complete closed-form solution to a tropical extremal problem
Abstract
A multidimensional extremal problem in the idempotent algebra setting is considered which consists in minimizing a nonlinear functional defined on a finite-dimensional semimodule over an idempotent semifield. The problem integrates two other known problems by combining their objective functions into one general function and includes these problems as particular cases. A new solution approach is proposed based on the analysis of linear inequalities and spectral properties of matrices. The approach offers a comprehensive solution to the problem in a closed form that involves performing simple matrix and vector operations in terms of idempotent algebra and provides a basis for the development of efficient computational algorithms and their software implementation.
Cite
@article{arxiv.1210.3658,
title = {A complete closed-form solution to a tropical extremal problem},
author = {Nikolai Krivulin},
journal= {arXiv preprint arXiv:1210.3658},
year = {2012}
}
Comments
Proceedings of the 6th WSEAS European Computing Conference (ECC '12), Prague, Czech Republic, September 24-26, 2012