A Note on Tropical Linear and Integer Programs

Peter Butkovič ()
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Peter Butkovič: University of Birmingham

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 3, No 17, 1026 pages

Abstract: 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.

Keywords: Tropical linear programming; Tropical integer programming; Duality; Residuation; 15A18; 15A80 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-018-1429-8

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