How to rewrite function to satisfy CVXPY ruleset (DCP error)?

Question

I have a quadratic program that CVXPY rejects because of DCP error. However I am certain that my formulation (see code below) satisfies the quadratic program (I'm trying to match this). I suspect it is due to how my functions are computed; Is there a way to rewrite it such that CVXPY (their ruleset) accepts it? Thanks.

def run_QP(n, p, L, Y, X, sigma, B_prop):
  
  # Configuring our inputs to suit LP
  Y_LP = Y.flatten('F')
  X_LP = np.zeros((n*L,p*L))
  for l in range(L):
    X_LP[n*l:n*(l+1),p*l:p*(l+1)] = X
  C_LP = np.eye(p)
  for l in range(L-1):
    C_LP = np.concatenate((C_LP, np.eye(p)), axis=1)
  one_p = np.ones(p)

  # Setting the objective matrix and vector
  constant = 1/(p*(sigma**2))
  P = constant * (X_LP.T @ X_LP)
  print('P\n',P)
  I_pL = np.eye(p*L)
  temp_term = -1*cp.log(B_prop[0]) * (one_p.T @ I_pL[0:p,:])
  for l in range(1,L):
    I_pL_trun = I_pL[p*l:p*(l+1),:]
    temp_term -= cp.log(B_prop[l]) * (one_p.T @ I_pL_trun)
  q = -1*constant*(Y_LP.T @ X_LP) + temp_term
  
  # Setting the equality constraints matrix
  A = np.concatenate((X_LP, C_LP), axis=0)
  # Setting the equality constraints vector
  b = np.concatenate((Y_LP, one_p), axis=0)

  # Define and solve the CVXPY problem.
  B_LP = cp.Variable(p*L)
  objective = cp.Minimize((1/2)*cp.quad_form(B_LP, P) + q.T @ B_LP)
  constraints = []
  constraints.append(A @ B_LP == b)
  problem = cp.Problem(objective, constraints)
  problem.solve()

  # Reconfiguring our outputs to suit pooled data
  B_QP_est = problem.value
  B_est = np.zeros((p,L))
  for l in range(L):
    B_col = B_QP_est[p*l:p*(l+1)]
    B_est[:,l] = B_col
  
  return B_est

B_bar_prob = [0.5,0.5]
L = 2
alpha = 0.5
p = 100
n = 20
sigma = 0.1

indices = np.random.choice(np.array([0, 1]), size=p, p=B_bar_prob)
B = np.eye(np.max(indices)+1)[indices]
X = binomial(1, alpha, (n, p))
Psi = normal(0, sigma, (n, L))
Y = np.dot(X, B) + Psi
B_prop = np.sum(B, axis=0) / n

B_hat = run_QP(n, p, L, Y, X, sigma, B_prop)

The error I get:

DCPError: Problem does not follow DCP rules. Specifically:
The objective is not DCP. Its following subexpressions are not:
QuadForm(var423, [[13.  7.  5. ...  0.  0.  0.]
 [ 7. 10.  4. ...  0.  0.  0.]
 [ 5.  4.  8. ...  0.  0.  0.]
 ...
 [ 0.  0.  0. ...  9.  5.  5.]
 [ 0.  0.  0. ...  5. 13.  6.]
 [ 0.  0.  0. ...  5.  6. 10.]])

How to rewrite function to satisfy CVXPY ruleset (DCP error)?

0 Answers0