# Support Vector Regression Implementation in CVX

Hello experts,

I am new to CVX. I might be overlooking the DCP set rules. But I do not manage to run the problem (related to support vector regression–please see the attachment) in CVX.

Updated (to make the software run):

``````clear variables
N   = 100;
M  = 2;
w  = [1;-1];     % weights
x  = randn(2,N); % input data
e  = randn(1,N); % noise
y  =  (w.')*x + e;
y  = y.';

lambda = 0.9;
eps = 0.5;
C   = 1/lambda;

cvx_begin
variables a(N) a_hat(N)
minimize( norm((sum(a-a_hat))*x, 2)  - ((a-a_hat)'*y) + eps * sum(a+a_hat) )
subject to
0 <= a  <= C;
0 <= a_hat  <= C;
sum(a) - sum(a_hat) == 0;
cvx_end
``````

Your help will be highly appreciated.

Additional questions: For some reasons, I can’t reply to Mark et al.
Instead of this cost " norm((sum(a-a_hat))*x, 2) ", I would like to implement with summation as given in the last part of eqn. (11.48) in the snapshot. Please suggest.

Thank you so much

I believe you want
`((a-a_hat)'*y')`
i.e., with transpose on y. That will at least be conformal, and accepted by CVX.

You also need to use `==` , not `=` for equality constraints, such as what you intended with `sum(a) - sum(a_hat) = 0;`

Those two changes will allow the program to run. I leave it to you to determine whether that solves the correct optimization problem. Perhaps you’re off by a factor of 1/2 on the norm term, as well as not having squared it, etc. You can determine whether these really matter to you.

Thank you for your help Mark!

Thank you again for your help, Mark. For some reasons, I could not reply. Now, it seems, I can do it.
Now, the program runs at least. I have one more question.

Instead of this cost " norm((sum(a-a_hat))*x, 2) ", I would like to implement with summation as given in the last part of eqn. (11.48) in the snapshot. Please suggest.

Your initial reply required moderator approval - perhaps an overactive spam filter or something.

You can apply `square_pos` to the `norm`, and then the multiplicative factor of 1/2.

I see. Thank you. I will try.

I don’t know where to ask, why my support-vector regression (SVR) implementation in CVX do not produce sensible results. I need to dig into it further. I need to compare it with the implementation in matlab toolboox.