Using loop to minimize the average in the objective function

1

Dear all,

I am trying to solve the following optimization problem using “for loop”. The code can successfully run, but I am not sure the way I used “for loop” for deriving the sum is correct or not since the outcome seems a little bit wired.

I would appreciate it if anyone could help me. Thanks!

Screenshot 2024-03-13 at 22.21.14
Screenshot 2024-03-13 at 22.21.142144×458 15.4 KB

obj=0;
N=100;
cvx_begin
    variable theta(6,2)
    for i=1:N
       obj=obj+quad_form( A' * theta' * x(:,i), Q )-z(:,i)' *A' * theta' * x(:,i) ;
    end
    minimize(obj2)
cvx_end
theta

where A and Q are 2 by 2, x is 6 by 1 and z is 2 by 1 with N scenarios.

2

it looks o.k. to me, except that there is a typo as written, (obj2 instead of obj) in the objective function. if you really ran it as written, then obj2 is a constant, and therefore the problem is minimizing a constant, which is the same as a feasibility problem, and because it is unconstrained, that means the solver and CVX can return whatever value of theta they want, and will consider the problem to be solved.

You didn’t divide by N, but the optimal theta should not be affected by that unless there are some numerical issues.

if you show the CVX and solver output, together with the optimal value of theta, perhaps someone can say something more.

3

if you really did run it with obj2, CVX might not even bother calling the solver, and might “solve it” analytically, populating theta with all zeros (or perhaps something else).

4

Thanks for taking time! I typed the code here wrongly where cvx is minimizing obj instead of ojb2. Appreciate a lot!