Cvxpy: DCPError : expr.is_dcp() returns False for expressions of the form w.T@w

[sadimanna]

Describe the bug
Any expression of the form x.T@P@x in cvxpy gives DCPError. When checked if the expression is DCP or not, expr.is_dcp() return False.

To Reproduce

import cvxpy as cp
import numpy as np

alphas = cp.Variable((2*NUM,1))
Cd = cp.Parameter()
Cd.value = 0.95

alphas_constraint_1 = [alphas[i] >=0 for i in range(2*NUM)]
alphas_constraint_2 = [alphas[i] <= Cd for i in range(2*NUM)]
alpha_y_constraint = [alphas.T@y == 0]

constraints = alphas_constraint_1 + alphas_constraint_2 + alpha_y_constraint

K = y[:,None]*x
K = np.dot(K,K.T)

objective_dual = cp.Minimize(-cp.sum(alphas)+alphas.T@K@alphas)

prob_dual = cp.Problem(objective_dual,constraints)

Expected behavior
As shown in various examples on the cvxpy tutorials, the above problem is expected to run without failure.

Version

• OS: Windows 10
• CVXPY Version: 1.1.0a3

Additional context
The problem I am trying to solve here is the dual form of SVM
Link to question posted on Stackoverflow

[SteveDiamond]

You need to use the quad_form atom, as in quad_form(x, P).

[akshayka]

@sadimanna , please read the documentation on DCP here: https://www.cvxpy.org/tutorial/dcp/index.html

DCP is a grammar for constructing convex expressions, using a simple composition rule. Once you learn this grammar (it's just one rule), you should be able to easily express essentially any convex expression in CVXPY.

[sadimanna]

You need to use the quad_form atom, as in quad_form(x, P).
@SteveDiamond @akshayka
I have tried using
-cp.sum(alphas)+0.5*cp.quad_form(alphas,K)
But I still get the same error

DCPError: Problem does not follow DCP rules. Specifically:
The objective is not DCP. Its following subexpressions are not:
QuadForm(var14052, [[ 1.83491803  1.75045974  2.28622267 ... -4.39732493 -5.00052443
  -3.77439719]
 [ 1.75045974  2.34203535  2.34179792 ... -5.44176538 -5.89979043
  -4.35890149]
 [ 2.28622267  2.34179792  2.8869991  ... -5.77716101 -6.50063002
  -4.88412578]
 ...
 [-4.39732493 -5.44176538 -5.77716101 ... 12.85096644 14.07871791
  10.45176273]
 [-5.00052443 -5.89979043 -6.50063002 ... 14.07871791 15.52527056
  11.56008668]
 [-3.77439719 -4.35890149 -4.88412578 ... 10.45176273 11.56008668
   8.61922173]])

I tried running this piece of code
expr = cp.quad_form(alphas,K) print(expr.curvature)

I get output UNKNOWN