Trying to convert Optimal ad problem to DPP

[w601sxs]

When I try the following example and check for dpp True:

# Generate data for optimal advertising problem.
import numpy as np
np.random.seed(1)
m = 5
n = 24
SCALE = 10000
B = np.random.lognormal(mean=8, size=(m,1)) + 10000
B = 1000*np.round(B/1000)

P_ad = np.random.uniform(size=(m,1))
P_time = np.random.uniform(size=(1,n))
P = P_ad.dot(P_time)

T = np.sin(np.linspace(-2*np.pi/2,2*np.pi  -2*np.pi/2,n))*SCALE
T += -np.min(T) + SCALE
c = np.random.uniform(size=(m,))
c *= 0.6*T.sum()/c.sum()
c = 1000*np.round(c/1000)
R = np.array([np.random.lognormal(c.min()/c[i]) for i in range(m)])

import cvxpy as cp

D = cp.Variable((m,n))
Si = [cp.minimum(R[i]*P[i,:]@D[i,:].T, B[i]) for i in range(m)]
prob = cp.Problem(cp.Maximize(cp.sum(Si)),
               [D >= 0,
                D.T @ np.ones(m) <= T,
                D @ np.ones(n) >= c])
prob.is_dpp()

Prints True

... But when I convert it to use parameters and variables like this:

# Problem scale
m = 5
n = 24
SCALE = 10000

B = cp.Parameter((m,1))

P = cp.Parameter((m,n))

T = cp.Parameter((n,))

c = cp.Parameter((m,))
R = cp.Parameter((m,))
D = cp.Variable((m,n))

Si = [cp.minimum(R[i]*P[i,:]@D[i,:].T, B[i]) for i in range(m)]

objective = cp.Maximize(cp.sum(Si))

constraints = [D >= 0,
               D.T @ np.ones(m) <= T, 
               D @ np.ones(n) >= c]

problem = cp.Problem(objective, constraints)

problem.is_dpp()

Prints False, so I can't build a layer with it.

[xkhainguyen]

In the first example, there are no cp parameters at all. Only one variable and everything else is constant. In the second example, you defined some cp parameters, your objective is definitely not DPP. Try to check the documents and use slack variables.