## How to automatically constrain some of the unknown values in an optimization problem?

### Rikke (view profile)

on 20 Mar 2019
Latest activity Commented on by Rikke

on 20 Mar 2019

### Torsten (view profile)

I have an optimization problem with several unknown values (x) which is a part of an array:
A=[0 0 x(1) x(2) 0 0 0 x(3) x(4) x(5) 0 0 0 x(6) 0 0 x(7) x(8)];
The x-values are to be optimized but each x-'group', which is separated by the zeros, are to be equal to each other. ex.: x(1)=x(2) and x(3)=x(4)=x(5) and so on. x(6) is not to be equal to another x because it is not in a 'group' with other x's, therfore x(6) will not be constrained.
I am supposed to write this constraint as ceq(x)=[..] in a constraint function.
Is there any automatic coding that can constrain these x-values in the way i explained?

### Torsten (view profile)

on 20 Mar 2019

If you know in advance which elements of the x-vector are grouped together, you can simply use Aeq and beq to define the equality constraints. No need to use the nonlinear constraints option in ceq.

Rikke

### Rikke (view profile)

on 20 Mar 2019
Thanks for your respond! I know which one is grouped together, but it will be time consuming because I actually have an array of 1740 elements with 55 of them as the unknown x-values. And I want the optimization model to work with any kind of array not only the one I have for the moment.
Matt J

### Matt J (view profile)

on 20 Mar 2019
@Rikke,
How are the groupings of the 55 unknowns specified as input? Do you have some sort of binary map?

on 20 Mar 2019
Edited by Matt J

### Matt J (view profile)

on 20 Mar 2019

I will assume you have some binary vector v which indicates the groupings of the variables, so for example this,
[0 0 x(1) x(2) 0 0 0 x(3) x(4) x(5) 0 0 0 x(6) 0 0 x(7) x(8)];
would be input as the vector
v=[0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1];
Then you can construct the linear equality constraint matrices Aeq, beq as follows
Aeq=diff(speye(numel(v)) ,1,1);
Aeq(:,~v)=[];
beq=zeros(size(Aeq,1),1);

Matt J

### Matt J (view profile)

on 20 Mar 2019
For the 8-variable example that you posted, this should result in
>> full(Aeq), full(beq).'
ans =
-1 1 0 0 0 0 0 0
0 0 -1 1 0 0 0 0
0 0 0 -1 1 0 0 0
0 0 0 0 0 0 -1 1
ans =
0 0 0 0
indicating that the first two unknowns will be equal, the next 3 unknowns will be equal and the final two unknowns will be equal.
Rikke

### Rikke (view profile)

on 20 Mar 2019
Thank you so much Matt J, it worked!