How to solve a system of linear equations with the following condition.

System of linear equations:

A * X = B

each x(i) belongs to the interval [0..max(i)], (max(i) - constants).

Simply speaking, all x(i) are positive values bounded by some known maximum values max(i).

How to solve this? I can easily make a system of non-linear equations out of it using some functions like max() and min() and solve it in Matlab as a system of non-linear equations, but I'm trying to find some simpler and "linear" way to solve it. So, can anyone remind me what is a classical approach for this in linear algebra?

Thanks for any hints!