TypeError in CVXPY: float() argument must be a string or a number, not 'Inequality'

Question

Still playing with CVXPY. This time I get an interesting error. Let us look at this minimal code

import cvxpy as cp
import numpy as np

A = np.random.normal(0, 1, (64,6))
b = np.random.normal(0, 1, (64,1))
theta = cp.Variable(shape = (6,1))

prob = cp.Problem(
    cp.Minimize(cp.max(A*theta -b) <= 5),
    [-10 <= theta, theta <= 10])

Once compiled, I get the following error:

~\Anaconda3\lib\site-packages\cvxpy\expressions\constants\constant.py in init(self, value) 42 self._sparse = True 43 else: ---> 44 self._value = intf.DEFAULT_INTF.const_to_matrix(value) 45 self._sparse = False 46 self._imag = None

~\Anaconda3\lib\site-packages\cvxpy\interface\numpy_interface\ndarray_interface.py in const_to_matrix(self, value, convert_scalars) 48 return result 49 else: ---> 50 return result.astype(numpy.float64) 51 52 # Return an identity matrix.

TypeError: float() argument must be a string or a number, not 'Inequality'

Answer 1

I don't know what you want to model exactly, but here something which works:

import cvxpy as cp
import numpy as np

A = np.random.normal(0, 1, (64,6))
b = np.random.normal(0, 1, (64,1))
theta = cp.Variable(shape = (6,1))

prob = cp.Problem(
            cp.Minimize(cp.sum(theta)),  # what do you want to minimize?
            [
                cp.max(A*theta -b) <= 5,
                -10 <= theta,
                theta <= 10
            ]
        )

works and should show the problem.

I would prefer a more clean impl like:

import cvxpy as cp
import numpy as np

A = np.random.normal(0, 1, (64,6))
b = np.random.normal(0, 1, (64,1))
theta = cp.Variable(shape = (6,1))

obj = cp.Minimize(cp.sum(theta))          # what do you want to minimize?
                                          # feasibility-problem? -> use hardcoded constant: cp.Minimize(0)
constraints = [
    cp.max(A*theta -b) <= 5,
    -10 <= theta,
    theta <= 10
]

prob = cp.Problem(obj, constraints)

The reason: it's easier to read out what's happening exactly.

Your problem: your objective has a constraint, which is impossible.

import cvxpy as cp
import numpy as np

A = np.random.normal(0, 1, (64,6))
b = np.random.normal(0, 1, (64,1))
theta = cp.Variable(shape = (6,1))

prob = cp.Problem(
cp.Minimize(cp.max(A*theta -b) <= 5),  # first argument = objective
                                       # -> minimize (constraint) : impossible!
    [-10 <= theta, theta <= 10])       # second argument = constraints
                                       # -> box-constraints

Shortly speaking:

• you want to minimize a function
• you do minimize an inequality

Towards comment below:

edit

obj = cp.Minimize(cp.max(cp.abs(A*theta-b)))

Small check:

print((A*theta-b).shape)
(64, 1)
print((cp.abs(A*theta-b)).shape)
(64, 1)

Elementwise abs: good

The final outer max results in a single value, or else cp.Minimize won't accept it. good

EDIT Or let's make cvxpy and us more happy:

obj = cp.Minimize(cp.norm(A*theta-b, "inf"))