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max-algebra; linear equations and inequalities; max-linear programming
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.
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