# Defining different bounds to each variable in fmincon

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Gábor Dupák on 18 Apr 2021
Commented: Gábor Dupák on 18 Apr 2021
Hi!
I have a nonlinear optimalization problem with 2 equality constraints and 3 variables (x1, x2, x3):
x1+0.13*x2*x3=50000;
0.7*x2-0.25x2*x3=60000;
where x1,x2 >=0 and 0>=x3>=1 are the uppern and lower bounds.
My objective function is MIN f(x)=0.4*x1+0.6*x2.
My question is how to define these bounds if i use fmincon?

Clayton Gotberg on 18 Apr 2021
The documentation for fmincon has the answer: you are allowed to pass upper and lower bounds as vectors.
For example,
lower_bound = [0 0 0];
upper_bound = [1 2 1];
Defines the boundaries for three inputs: the first between 0 and 1, the second between 0 and 2, and the third between 0 and 1. I believe that you can fill in Inf or -Inf for a boundary as well.
I would also check on the boundaries you quote in your post. 0>=x3>=1 is impossible, as it says that x3 must be less than or equal to 0 but also greater than or equal to 1.
Gábor Dupák on 18 Apr 2021
Thanks for you help! Yes, I miswrote the x3 bounds, of course I wanted as: 0<=x3<=1.