How to define the weighted norm of a vector?

[Saeed]

Hello.

I've seen that the following is used as the objective function in MPC example in Yalmip.

objective = objective +  norm(Q*x{k},1) + norm(R*u{k},1)

Does (Q*x{k},2) is identical  to x{k}' * Q * x{k}?

I couldn't find it in norm command page.

Thanks.

[Johan Löfberg]

No. Norm follows matlab (and math in general) standard norm definition, so norm(x,2) = sqrt(sum(x.^2)) = sqrt(x'*x) which means norm(Q*x,2) will be sqrt(x'*Q'*Q*x)

[Saeed]

As I've observed,

x{k}' * Q * x{k} is identical to (norm(Q^(0.5)*x , 2))^2.

Am I right?

[Johan Löfberg]

Yes, by the definition of the Euclidean norm.

[Saeed]

Thanks very much for your support.

Regards.