Optimizing two vectors of different sizes

I am working to optimize the following problem:

r=optimvar('r',size(S,1),'LowerBound',0,'UpperBound',1);
B= optimvar ('B', size(dm,2));
p=prob2matrices({r, B},'Constraints', sum(r)<=1);


%Solving optimization problem
Roptimal=lsqlin([S', 1], dm(:), p.Aineq,p.bineq,[],[],p.lb,p.ub)

Where S is a n x m matrix, and dm is a m x 1 matrix. The result is that r (n x 1 natrix) and B (m x 1 matrix) are different sizes, and cannot be concatenated. The equation I am essential trying to solve is as follows:

%minimize "e2"
e= dm - (S'*r+B)
e2= e*e'

I recogonize I am probably not using an appropriate function. Any help would be greatly appreciated.

[Nagasai Bharat]

Hi,

From the equation (r' * S) would be a 1 x m matrix whereras B is a m x 1 matrix. Try to cross-check as a transpose of B would be needed to have an addition operation.

[Adam Rish]

So I adjusted my inputs, but am still getting the same error. Here is what I've written

r=optimvar('r',size(S,1),'LowerBound',0,'UpperBound',1);
p=prob2matrices({r},'Constraints', sum(r)<=1);
%Solving optimization problem
Roptimal=lsqlin([S', I], dm(:), p.Aineq,p.bineq,[],[],p.lb,p.ub)

So the equation I am trying to solve/minimize using lsqlin is the following:

S'*r+B-dm

Where I am trying to solve for r (n x 1 matrix) and B. S is still a n x m matrix, and dm is a 1 x m matrix. S'*r is therefore a m x 1 matrix. The problem is that I need B to be an m x 1 matrix but the requirement of multiplier I seems to prevent me from doing that

Answer 1

[Matt J]

r=optimvar('r',n,'LowerBound',0,'UpperBound',1);
B= optimvar ('B', m);
[p,idx]=prob2matrices({r, B},'Constraints', sum(r)<=1);

C=nan(m,m+n);
C(:,idx.r)=S';
C(:,idx.B)=eye(m);

Roptimal=lsqlin(C, dm(:), p.Aineq,p.bineq,[],[],p.lb,p.ub);

sol=x2sol(Roptimal,idx), %solution