Inequality constraints in least-squares fitting

I would like to perform least-squares fitting with inequality constraints that involve the parameters in both sides, in addition to box constraints (bounds). For example, for a 2 parameter (x1, x2) problem I would need to something like:

lb = [0, 0];
up = [100, 100];
x1 >= x2;
x1 <= x2*5;

I am typically using lsqnonlin but I understand this is not possible with this function. Is there another way to do this, and how can I set it up? Many thanks.