Geodesic
Simultaneous solution of linear equations and inequalities in max-algebra
Kybernetika, Tome 47 (2011) no. 2, pp. 241-250.

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Let $a øplus b=\max(a,b)$ and $a øtimes b = a+b$ for $a,b\in{\mathbb{R}}$. Max-algebra is an analogue of linear algebra developed on the pair of operations $(øplus, øtimes)$ extended to matrices and vectors. The system of equations $A øtimes x=b$ and inequalities $C øtimes x łeq d$ have each been studied in the literature. We consider a problem consisting of these two systems and present necessary and sufficient conditions for its solvability. We also develop a polynomial algorithm for solving max-linear program whose constraints are max-linear equations and inequalities.
Classification : 15A06, 15A39, 90C26, 90C27
Keywords: max-algebra; linear equations and inequalities; max-linear programming 
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     author = {Aminu, Abdulhadi},
     title = {Simultaneous solution of linear equations and inequalities in max-algebra},
     journal = {Kybernetika},
     pages = {241--250},
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     number = {2},
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     zbl = {1222.15002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2011__47_2_a4/}
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Aminu, Abdulhadi. Simultaneous solution of linear equations and inequalities in max-algebra. Kybernetika, Tome 47 (2011) no. 2, pp. 241-250. http://geodesic.mathdoc.fr/item/KYB_2011__47_2_a4/