Schur complement implemented in complex variables

(Echo Shaun) #1

when schur complement implemented in cvx, there always made a ‘inf’ result.
just like the formulation

, where Q equals 1, is invertible and positive semidefinite and P equals a constant value eqauls -3, S is a purely imaginary variable equals 1j ,similarly conj(S) equals -1j.
by implementing schur complement, I wanna transfer the inequality constraints to semidefinite programming, which is as follows:
abs(S).^2 -P >=0.
thanks for anybody teaching!!

(Mark L. Stone) #2

You can’t do anything with Schur complement or semidefinite constraint with one positive diagonal element and one negative diagonal element. That is an indefinite matrix.

Another way of seeing that is that abs(S).^2 -P >= 0 is a non-convex constraint.

(Echo Shaun) #3

Thanks Mark. maybe I have to reformulate such problem in an sdp acceptable approach.