Why am I getting this DCPError when my matrix is PSD?

Question

import cvxpy as cp
import numpy as np

n = 3
PP = cp.Variable((n,n),"PP")
KK = [[2,1,3],[1,2,1],[3,1,2]]
s = np.array([[.1, .4, .5]]).T
t = np.array([[.4, .2, .4]]).T
e = np.ones((n,1))
x = PP.T@e - s
y = PP@e - t
for b in range(1,21):
    obj = (1/4/b) * (cp.quad_form(x,KK) + cp.quad_form(y,KK)) - cp.trace(KK@PP) 
    prob = cp.Problem(cp.Minimize(obj),[PP>=0,cp.sum(PP)==1])
    obj=prob.solve()
    print("status:",prob.status)
    print("obj:",obj)
    print(PP.value)

When I run this, I get

cvxpy.error.DCPError: Problem does not follow DCP rules. Specifically:
The objective is not DCP. Its following subexpressions are not:
QuadForm(PP.T * [[1.]
 [1.]
 [1.]] + -[[0.1]
 [0.4]
 [0.5]], [[2. 1. 3.]
 [1. 2. 1.]
 [3. 1. 2.]])

I don't see why I'm getting this error when my matrix KK is clearly PSD. Why is this happening?

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Duplicate here at https://stackoverflow.com/q/60745793/649090

Answer 1

Because the matrix KK is not PSD. It has minimum eigenvalue of -1. It is indefinite.

Perhaps you are under the misapprehension that a symmetric matrix with all elements positive is PSD. As this example shows, that is not the case.