constrain variables to a set of values

I have two questions.

My objective finction is L*A (dot product).

I want to optimze my variables which are in matrix (A). But the elemnts of the output of optimizing A should be one value from a set of specific values.

For example: I want to set the output values of A (after the optimization) to be one of the following values { 1:37}.

1) how can I set that the elemnts of the output matrix (A) to be one of the values from the givien set?

And one more thing. I have a ready function (pfile) which I want to use in the optimization problem. That function works as follow:

[w, a, x] = ASU(A)

I get 3 outputs from that function and I would like to minimize my objective function subjected to the output (a) and (x) =0.

2) how can I use the output of the given ASU function as contraints to the optimization problem?

The problem is linear and I am using solver-based.

L is 345x1

A is 1x345

w,a and x are 1x1

ASU accepts only a 1x345 matrix.

If I multiple L*A by a constant (density) it will give me w which is the objective function that I want to minimize

Thanks

[Matt J]

What are the sizes of everything A, L,a,x,w? Is w the objective function value L*A?

[Omar Morsy]

A is 1x345 / L is 345x1 / a,x and w are 1x1 / and if I multiple L*A by a constant (density) it will give me w which is the objective function.

[Matt J]

A is 1x345 / L is 345x1

If so, then L*A gives a 345x345 matrix, not a scalar objective value. Is your objective meant to be L.' *A.' ?

[Omar Morsy]

It is a dot product of L and A.

I forgot to clarify that.

[Omar Morsy]

I edited my question to clarify all the missing data

Answer 1

[Matt J]

The first thing I recommend is that you use ASU to compute L and the equality constraints in matrix form. You can do that by downloading func2mat,

https://www.mathworks.com/matlabcentral/fileexchange/44669-func2mat-convert-linear-function-to-matrix

M=func2mat(@fun,zeros(345,1))

L=M(1,:);
Aeq=M(2:3,:);

function out=fun(A)
 
  [w,a,x]=ASU(A);
   out=[w;a;x];
  
end

Now you make the change of variables A=Z*[1.6; 2.1; 2.2; 17.2] where Z is a 345x4 unknown binary matrix satisfying sum(Z,2)=1. You then solve for Z with intlinprog,

v=[1.6; 2.1; 2.2; 17.2];

f=kron(v',L);

Aeq=kron(v', Aeq); %a=0 and x=0
beq=[0;0];

Aeq=[Aeq;  kron([1,1,1,1], speye(345))]; %sum(Z,2)=1
beq(3:347)=1;

lb=zeros(345,4);

Z=intlinprog(f,1:numel(lb),[],[],Aeq,beq,lb,lb+1);

A=Z*v;

[Omar Morsy]

I already got the matrix L. I don’t want to use func2mat. So what’s the alternative solution for that?

[Matt J]

You should use func2mat. The alternative is to use ga() which will let you implement your objective and constraints in functional form, but I expect that will be less reliable. ga() will have no way of knowing that your problem is linear, and will be forced to use a more generic solution method.

[Omar Morsy]

When I run the first line of the code. I get the following error :-

Unrecognized function or variable 'fun'.

Error in func2mat (line 77)

T=fun(Xtypical);

[Matt J]

For some reason, fun() is not visible to Matlab. Why that happens depends on where you put it.

function out=fun(A)
 
  [w,a,x]=ASU(A);
   out=[w;a;x];
  
end

[Omar Morsy]

I used the same order that you commented in your first comment.

M=func2mat(@fun,zeros(345,1))

L=M(1,:);

Aeq=M(2:3,:);

function out=fun(A)

[w,a,x]=ASU(A);

out=[w;a;x];

end

and this is what I get.

Error in func2mat (line 77)

T=fun(Xtypical);

Error in Untitled4 (line 21)

M = func2mat(@fun,zeros(345,1));

[Matt J]

That is different from the first error that you showed.

[Omar Morsy]

The first error was after just using

M=func2mat(@fun,zeros(345,1))

But the second was when I used the whole code. And in both of them

Error in func2mat (line 77)

T=fun(Xtypical);

this error is common

[Matt J]

But the first line was the same in both cases, so they should have thrown the same error.

[Matt J]

Also, it looks like you only printed part of the error message.

[Omar Morsy]

yes there was an error in using the ready function.

Thats the full error msg

Error using ASU

"Sections" should be a row vector [1x345]

Error in Untitled4>fun (line 27)

[w,s,d] = ASU(S,0);

Error in func2mat (line 77)

T=fun(Xtypical);

Error in Untitled4 (line 21)

M = func2mat(@fun,zeros(345,1));

[Matt J]

Change to

M=func2mat(@fun,zeros(1,345));

[Omar Morsy]

That did not solve the issue. These are the new errors.

Error using ASU

Sections should be integer values between 1 and 37

Error in Untitled4>fun (line 27)

[w,s,d] =ASU(S,0);

Error in func2mat (line 77)

T=fun(Xtypical);

Error in Untitled4 (line 21)

M = func2mat(@fun,zeros(1,345));

[Matt J]

I have been assuming (because you said your problem was linear) that ASU is linear and therefore is defined for any input A. Yet, it complains when we give it zeros as input. Is ASU linear? Should it return 0 for an input of 0 (as any linear function should)?

[Omar Morsy]

Yes it is linear

[Matt J]

If it truly is linear, then this should fix it.

A1=ones(1,345);
wax1=fun(A1);

M=func2mat(  @(A)fun(A+1) - wax1 ,  A1);

L=M(1,:);
Aeq=M(2:3,:);


function out=fun(A)
 
  [w,a,x]=ASU(A);
   out=[w;a;x];
  
end