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

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

Matt J on 20 Mar 2019
Edited: Matt J 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);
##### 2 CommentsShow 1 older commentHide 1 older comment
Rikke on 20 Mar 2019
Thank you so much Matt J, it worked!

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