MATLAB: How to automatically constrain some of the unknown values in an optimization problem

arrayautomatically constrainceqconstraintoptimizationOptimization Toolbox

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?

Best Answer

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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MATLAB: How to make some optimization variables equal to each other

I assume you are using one of the MATLAB optimization functions such as fmincon or linprog. These functions include arguments Aeq,beq for equality constraints. I'm not quite clear about your indexing and the dimension of the vector x that you are trying to optimize. I think you are looking for a length twelve vector where some of the values are forced to zero and others must be equal to each other. If this is the case you could use these to enforce the constraints that you have, for example as follows:

Aeq = [1 -1 0  0  0 0  0 0 0 0 0 0;
       0  0 1 -1  0 0  0 0 0 0 0 0;
       0  0 1  0 -1 0  0 0 0 0 0 0;
       0  0 0  0  0 1 -1 0 0 0 0 0;
       0  0 1  0  0 0  0 0 0 0 0 0;
       0  0 0  0  0 1  0 0 0 0 0 0;
       0  0 0  0  0 0  1 0 0 0 0 0;
       0  0 0  0  0 0  0 1 0 0 0 0;
       0  0 0  0  0 0  0 0 0 0 0 1]
beq = zeros(9,1)

so the first four rows enforce your constraints where one element has to equal another and the other 5 rows force elements of x to be equal to zero.

I would suggest though that it would be better to reformulate your problem to not have these zeros included, since you already know what there value is. In this case you would only need a length seven vector x and you could have

Aeq = [1 -1 0  0  0 0  0;
       0  0 1 -1  0 0  0;
       0  0 1  0 -1 0  0;
       0  0 0  0  0 1 -1 ]
beq = zeros(4,1)

MATLAB: Creation of multiple rectangles

Hi,

You can use patch function for this purpose.

Oleg in the following answer explains how that can be achieved.

https://www.mathworks.com/matlabcentral/answers/158482-faster-way-to-create-rectangles

Hope this helps!

Best Answer

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MATLAB: How to make some optimization variables equal to each other

MATLAB: Creation of multiple rectangles

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