Complete solution of a constrained tropical optimization problem with application to location analysis
Optimization and Control
2014-04-17 v2 Systems and Control
Abstract
We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means of a conjugate transposition operator, subject to constraints in the form of linear vector inequalities. A complete direct solution to the problem under fairly general assumptions is given in a compact vector form suitable for both further analysis and practical implementation. We apply the result to solve a multidimensional minimax single facility location problem with Chebyshev distance and with inequality constraints imposed on the feasible location area.
Cite
@article{arxiv.1311.2795,
title = {Complete solution of a constrained tropical optimization problem with application to location analysis},
author = {Nikolai Krivulin},
journal= {arXiv preprint arXiv:1311.2795},
year = {2014}
}
Comments
20 pages, 3 figures