Adding constraint to ensure diagonals of a complex matrix are equal?

Asked May 18 '23 at 15:13

Active May 18 '23 at 15:14

Viewed 41 times

I'm trying to solve a convex minimzation problem using the CVXPY module in Python. I want to solve for a complex matrix X of dimension d*d and add the Constraints, that trace (A * X) = 1 for a given matrix A and X is positive semdefinite, hermitean and all diagonal entries of X are equal to one another.

I added the first 3 Constraints into my Code by

X = cp.Variable((d,d), complex = True)
constraints = [X >>0, cp.trace(A @ X) == 1]

Does anyone have any idea how to add the last constraint, that all diagonal elements are equal?

edited May 18 '23 at 15:14

Jonathan Hall

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asked May 18 '23 at 15:13

BB27pscl

Can't you declare that `X` is PSD? Why impose that constraint later? – Rodrigo de Azevedo May 18 '23 at 15:22
I can only add one attribute in the declaration of my variable X, so i was thinking i had to add the fact that X is complex. – BB27pscl May 19 '23 at 21:35
Just add the constraints one by one (X[i,i]==X[0,0]) or use cp.diag() – Michal Adamaszek May 22 '23 at 08:26
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Thank you, I added the constraint by cp.diag(X) == X[0,0] * np.ones(d) – BB27pscl May 23 '23 at 10:57

Adding constraint to ensure diagonals of a complex matrix are equal?

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