A note on systems with max-min and max-product constraints

We consider a system A ◦ x b, where A ∈ Rm×n + is a non-negative matrix and b ∈ R+ is a non-negative vector over the n-dimensional variable l x u, where l, u ∈ R+ are lower and upper bounds, respectively, and ◦ is either a max–min or a maxproduct composition. It is shown that the set of minimal solutions of such systems can be computed in incremental quasi-polynomial time. © 2008 Elsevier B.V. All rights reserved.