least square minimization with strict inquality constraint

I have a least square minimization problem with a constraint of the form Ax<=b. Even though, in principle the condition "=" in A<= b is allowable, the fact that algorithm converges to a solution with all zero values is not desirable. Is there any way to enforce strict inequality in matlab function lsqlin() ? Specifically, I use some equations of the inequality constraint equation, Ax<=b, to ensure x is less than zero,negative, like x2<0, x3<0. Along with that I have other constriants like -(x1+x2+x3)<=0 with x1>0. In all these cases I prefer a solution with strict inequality constriant. Waiting for any kind suggestions.

Thanking you!

[Ced]

If you want to ensure x2 < 0 instead of x2 <= 0, just insert a small bias, i.e. x2 <= -1e-7.

[reen2015]

Thank you Ced for your kind reply.