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

We consider a system A o x >= b, where A is an element of R-+(mxn) is a non-negative matrix and b is an element of R-+(m) is a non-negative vector over the n-dimensional variable l <= x <= u, where l, u is an element of R-+(n) are lower and upper bounds, respectively, and o 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. (C) 2008 Elsevier B.V. All rights reserved.