On Tropical Linear and Integer Programs
Optimization and Control
2017-09-27 v1
Abstract
We present simple compact proofs of the strong and weak duality theorems of tropical linear programming. It follows that there is no duality gap for a pair of tropical primal-dual problems. This result together with known properties of subeigenvectors enables us to directly solve a special tropical linear program with two-sided constraints. We also study the duality gap in tropical integer linear programming. A direct solution is available for the primal problem. An algorithm of quadratic complexity is presented for the dual problem. A direct solution is available provided that all coefficients of the objective function are integer. This solution yields a good estimate of the optimal objective function value in the general case.
Cite
@article{arxiv.1709.08983,
title = {On Tropical Linear and Integer Programs},
author = {Peter Butkovic},
journal= {arXiv preprint arXiv:1709.08983},
year = {2017}
}