Questions regarding diagonally dominant matrix

[Etienne G.]

Dear Prof. Löfberg,

I am trying to approximate an SDP problem by its DD counterpart. I read the code you provide in the "dd.m" file but I'm not sure I understand it correctly.

For the second constraint, diag(X) >= sum(Z,2), I can see where it comes from, no problem.

But what about the first constraint? What do W and Z correspond to?

Thanks very much for your reply !

Etienne

[Johan Löfberg]

Did you find that function by luck? I did not remember it existed and have no memory of it being publically announced

Anyway, looking at the code, the variable Z is an epigraph representation of the nondiagonal elements (i.e. W) of X. Hence, diagonal larger than sum of absolute values of non-diagonal elements

[Etienne G.]

Thanks for your reply,

I wasn't specifically looking to use Yalmip for this problem but simply tried "open dd" on Matlab and found this function in Yalmip.

To complete your answer, why not just use a single constraint "diag(X) >= sum(abs(Z),2)" I feel like it's the same thing, right?

Best,

Etienne

[Johan Löfberg]

Yes, but that just means YALMIP has to derive the model for the absolute value in another layer downstream, so why not do it immediately so no analysis etc has to be done later