# Is there a way to realize the equality constraint which is a concave in the left side?

How to realize the following problem using cvx.
variable x(Ng,Ng) hermitian semidefinite;
minimize(sum(sum(abs(x),1),2)+lambdasum(sum_square_abs(Ryu-Audiag(x)*(Au’)),2));
subject to
for k=1:Ng
for n=k:Ng
det_rootn([x(k,k),x(k,n);x(n,k),x(n,n)])==0;
end
end
where x is the optimization variable;Ryu,Au are deterministic matrixs respectively; lambda is a regularization parameters.
Maybe the most troublesome problem is to realize the equality constraint .

1 Like

Equalities must be linear. End of story.

That’s a whole lot of singularity going on.

You are attempting to constrain every 2 by 2 submatrix of a hermitian semidefinite matrix to be singular. The only possibility I can think of to reformulate this as a convex problem is if there is a reparameterization of `x` in a lower dimensional space such that singularity constraints are not needed. I have no idea whether that can be done.

Do you really want all the non-principal 2 by 2 submatrices to be singular, or just the 2 by 2 principal submatricss? And of course, the n = k constraints can be eliminated as vacuous.