We propose an efficient method for finding a Chebyshev-best soluble approximation to an insoluble system of linear equations over max-plus algebra.

A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.

This paper demonstrates that the sensor cover energy problem in wireless communication can be transformed into a linear programming problem with max-plus linear inequality constraints. Consequently, by a well-developed preprocessing procedure, it can be further reformulated as a 0-1 integer linear programming problem and hence tackled by the routine techniques developed in linear and integer optimization. The performance of this two-stage solution approach is evaluated on a set of randomly generated...

In max-min algebra the standard pair of operations plus and times is replaced by the pair of operations maximum and minimum, respectively. A max-min matrix $A$ is called strongly robust if the orbit $x,A\otimes x,A^2\otimes x,\cdots$ reaches the greatest eigenvector with any starting vector. We study a special type of the strong robustness called the strong X-robustness, the case that a starting vector is limited by a lower bound vector and an upper bound vector. The equivalent condition for the strong X-robustness is introduced...