A note on tropical linear and integer programs

Peter Butkovic

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1 Citation (Scopus)
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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.
Original languageEnglish
Pages (from-to)1011-1026
Number of pages16
JournalJournal of Optimization Theory and Applications
Issue number3
Early online date2 Nov 2018
Publication statusPublished - Mar 2019


  • Tropical linear programming
  • Tropical integer programming
  • Duality
  • Residuation


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