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We present a new, simple compact proof of the known strong duality theorem of tropical linear programming with one-sided constraints. This result together with 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 provides a good estimate of the optimal objective function value in the general case.
|Number of pages||16|
|Journal||Journal of Optimization Theory and Applications|
|Early online date||2 Nov 2018|
|Publication status||Published - Mar 2019|
- Tropical linear programming
- Tropical integer programming
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- 1 Finished
Perron-Frobenius Theory and Max-Algebraic Combinatorics of Nonnegative Matrices
Engineering & Physical Science Research Council
12/03/12 → 11/03/14
Project: Research Councils