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Abstract
We present a new, simple compact proof of the known strong duality theorem of tropical linear programming with onesided constraints. This result together with properties of subeigenvectors enables us to directly solve a special tropical linear program with twosided 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 language  English 

Pages (fromto)  10111026 
Number of pages  16 
Journal  Journal of Optimization Theory and Applications 
Volume  180 
Issue number  3 
Early online date  2 Nov 2018 
DOIs  
Publication status  Published  Mar 2019 
Keywords
 Tropical linear programming
 Tropical integer programming
 Duality
 Residuation
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Dive into the research topics of 'A note on tropical linear and integer programs'. Together they form a unique fingerprint.Projects
 1 Finished

PerronFrobenius Theory and MaxAlgebraic Combinatorics of Nonnegative Matrices
Butkovic, P.
Engineering & Physical Science Research Council
12/03/12 → 11/03/14
Project: Research Councils