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A Note on Tropical Linear and Integer Programs

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  • Peter Butkovič

    (University of Birmingham)

Abstract

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.

Suggested Citation

  • Peter Butkovič, 2019. "A Note on Tropical Linear and Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 1011-1026, March.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:3:d:10.1007_s10957-018-1429-8
    DOI: 10.1007/s10957-018-1429-8
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    References listed on IDEAS

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    1. A. J. Hoffman, 1963. "On abstract dual linear programs," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 10(1), pages 369-373, March.
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