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

We consider a system A∘x⩾b, where is a non-negative matrix and is a non-negative vector over the n-dimensional variable l⩽x⩽u, where are lower and upper bounds, respectively, and ∘ is either a max–min or a max-product composition. It is shown that the set of minimal solutions of such systems can be computed in incremental quasi-polynomial time.