A note on tropical linear and integer programs

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Colleges, School and Institutes

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.

Details

Original languageEnglish
Pages (from-to)1011-1026
Number of pages16
JournalJournal of Optimization Theory and Applications
Volume180
Issue number3
Early online date2 Nov 2018
Publication statusPublished - Mar 2019

Keywords

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