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arXiv · 1709.08983

On Tropical Linear and Integer Programs

Peter Butkovic
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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.

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Peter Butkovic. 2017-09-26. On Tropical Linear and Integer Programs. https://arxiv.org/abs/1709.08983

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