Rank of Matrix in cvx

1

Rank（X）<1,
Hello, I want to express the rank of the matrix in the constraints, how to express this rank()

2

There are only very limited types of rank constraints which are convex and compatible with CVX. You can read about them in https://convexoptimization.com/TOOLS/0976401304.pdf . Warning, that book is not easy reading, and I can’t vouch that everything in it is correct.

A typical constraint such as rank(X) == 1 is non-convex, and sometimes is relaxed, i.e., ignored, in order to make a problem convex and formulatable in CVX. If you really need rank(X) == 1, that is non-convex, and you can try using YALMIP.

3

Why is rank (X) ==1 non-convex?

4

You should tell us why it is.

But it isn’t, as this simple counterexample shows.

A=[1 2;2 4];
B=[1 1;3 3];
disp(rank(A))
     1
disp(rank(B))
     1
disp(rank(.5*A+.5*B))
     2
5

Yes, Exactly Sir. resultant one is not in the rank=1 space. Hence it is non-convex