Matrix inequality on a 3D sdpvar

[mkdeak]

Hi-

I understand that YALMIP detects symmetry in order to decide whether to treat the constraint A >= 0 as an element-wise inequality or a matrix inequality.

Suppose I declare a 3 dimensional sdpvar which consists of k pages of n by n matrices:

As = sdpvar(n, n, k);

Now every page As(:,:,i) of As is an symmetric matrix variable, however the constraint As >= 0 gets interpreted as an element-wise inequality. How can I have this constraint interpreted as a semidefinite constraint on each of the pages of As?

A second question I have is this: assume that B is some fixed n by n matrix which is symmetric. I would like to further assert that B * As(:, :, i) >= 0 for each index i. I have already implemented a helper function that does the matrix multiplication page-wise by reshaping As. So suppose my_pagemtimes is this helper function. I would like the assertion

my_pagemtimes(B, As) >= 0

to be regarded as another matrix inequality instead of element-wise inequalities. Since B is symmetric and so are all the pages of As, each page of the left hand side is symmetric here as well. Yet YALMIP regards this as an element-wise inequality. How can I make this work?

[johanlofberg]

That is probably not intended behavior, and will have to be fixed. For now, you will have to loop over the slices

BA where B and A are symmetric does not mean BA is symmetric. Here you will have to loop regardless though, as nd-array matrix multiplications simply isn't supported

[mkdeak]

Thanks for the quick reply. And yes, I got that wrong for the second question... thanks for pointing it out.