error using2 norm insid quad_form in objective function

[Sandeep hegde]

Hello members,

I want to add this term to my objective function

Wij( || X- Y ||_2 - D)^2

where Wij, D are scalars. ||X-Y||_2 is 2-norm, X&Y are vectors of size 3. If I make the below formulation in cvxpy, I get an error:

import cvxpy as cp

import numpy as np

x = cp.Variable(3)

Y = np.array([1,2,3])

term = cp.norm(x- Y,2)-D

cost = 10*cp.quad_form(term,1)

# constraints not shown, but correctly in place

problem = cp.Problem(cp.Minimize(cost),constraints)

problem.solve(verbose = True,solver='OSQP')

raise ValueError("Invalid dimensions for arguments.")
ValueError: Invalid dimensions for arguments.

Is this formulation correct, allowed? If not, how can I change this? In the second argument of quad_form instead of 1, I tried np.eye(1) but it doesn't help. Can someone kindly guide me?

Thank you

Sandeep

[Michal Adamaszek]

You can only have affine expressions in quad_form. Also, the term you are trying to create is not convex.

Michal

[Sandeep hegde]

Hi Mr. Adamaszek,

Thanks for your reply. I have a question again: I have a constraint || X- Y ||_2 >= D which can be also written equivalently as (|| X- Y ||_2 - D)^2 according to this research paper (please see the attachment). I have to include this term in my objective function which also contains some other quadratic terms already. Is there any way to do this in cvxpy? If I consider norm function in cvxpy, then it cannot be reduced to QP anymore.

Thank you in advance

Sandeep

[Michal Adamaszek]

Sorry but I don't see how to make any mathematical sense of the highlighted statement. 

[Sunghee Yun]

Hi Sandeep,

In addition to Michal's comment above, the constraints, $\|X_i - X_j^P\|_2 \geq D" is not convex constraints, hence cvxpy wouldn't accept it.

Best,

Sunghee