Minimising with multiple constraints and then storing them using a loop

I want to minimize a function with two inequality constraints and different set of parameters.

min -x1*x2*x3 

st 
 –a11*x1–a12*x2–a13*x3 ≤ b1;
  a21*x1+a22*x2+a23*x3 ≤ b2

I have 100 different A=[a11 a12 a13; a21 a22 a23] matrices and 100 different b=[b1;b2] vectors. For each pair of matrix A and vector b, I will have one solution x=(x1 x2 x3).

My goal is to have a single data set with all the solutions of all the inequality constraints. I mean the first row of that x will have the solution for 1st A,b the the 2nd row for next A,b and so on.

Can anyone please help, thank you so much.

[Matt J]

My goal is to have a single data set with all the solutions of all the inequality constraints. I mean the first row of that x will have the solution for 1st A,b the the 2nd row for next A,b and so on.

It's usually better to store things column-wise in MATLAB (as in my Answer below) since memory access is faster for columns.

[econgrad]

ok I see, thanks.

Answer 1

[Matt J]

Should be pretty straightforward. The code will look like,

   X=zeros(3,100);

   for i=1:100

    X(:,i)=fmincon(@(x)-prod(x), InitialGuess,A(:,:,i),b(:,i));

   end

[econgrad]

Thank you Matt, let me give it a try and I will post my comments.

[econgrad]

Matt, why do I have to use prod(x)? Also, is A(:,:,i) pick up all the rows corresponding to i th col? Sorry,in my original question I forgot to post that the A matrix I have looks like this: A=[1 2 3;2 3 4;4 1 2;1 2 4]so the first two rows will be the constraint matrix for the first problem, the next two rows for the second problem and so on. Similarly the b vector and the x0 vector are also arranged that way. I hope I have explained this properly. Thank you so much for your help.

[Matt J]

why do I have to use prod(x)?

Isn't it appropriate? In the problem you posted, the objective is the product of all the variables (times -1).

Also, is A(:,:,i) pick up all the rows corresponding to i th col?

Yes, but it was just an example. Extract the linear inequality constraint data for the i-th problem in whatever way suits the way you have your data organized.