Solver 'CVXOPT' failed when solving LP

[GrahamHulsey]

CVXPY is unable to solve a simple LP with solver set to CVXOPT
I am running cvxpy and cvxopt in a virtual environment on Ubuntu 22.04.4. After successfully pip installing both cvxpy and cvxopt, I ran the following model:

import cvxpy as cp
import numpy as np
import cvxopt


n = 2
x = cp.Variable(n)

prob = cp.Problem(cp.Maximize(cp.sum(x)), [cp.sum(x) <= 10])
prob.solve(solver=cp.CVXOPT, verbose=True)

print("\nThe optimal value is", prob.value)
print("A solution x is")
print(x.value)
print("A dual solution is")
print(prob.constraints[0].dual_value)

This gives the following output:

CVXPY                                     
v1.4.3                                    

(CVXPY) Apr 17 09:46:13 PM: Your problem has 2 variables, 1 constraints, and 0 parameters.
(CVXPY) Apr 17 09:46:13 PM: It is compliant with the following grammars: DCP, DQCP
(CVXPY) Apr 17 09:46:13 PM: (If you need to solve this problem multiple times, but with different data, consider using parameters.)
(CVXPY) Apr 17 09:46:13 PM: CVXPY will first compile your problem; then, it will invoke a numerical solver to obtain a solution.
(CVXPY) Apr 17 09:46:13 PM: Your problem is compiled with the CPP canonicalization backend.

Compilation                                  

(CVXPY) Apr 17 09:46:13 PM: Compiling problem (target solver=CVXOPT).
(CVXPY) Apr 17 09:46:13 PM: Reduction chain: FlipObjective -> Dcp2Cone -> CvxAttr2Constr -> ConeMatrixStuffing -> CVXOPT
(CVXPY) Apr 17 09:46:13 PM: Applying reduction FlipObjective
(CVXPY) Apr 17 09:46:13 PM: Applying reduction Dcp2Cone
(CVXPY) Apr 17 09:46:13 PM: Applying reduction CvxAttr2Constr
(CVXPY) Apr 17 09:46:13 PM: Applying reduction ConeMatrixStuffing
(CVXPY) Apr 17 09:46:13 PM: Applying reduction CVXOPT
(CVXPY) Apr 17 09:46:13 PM: Finished problem compilation (took 2.648e-03 seconds).

Numerical solver                               

(CVXPY) Apr 17 09:46:13 PM: Invoking solver CVXOPT  to obtain a solution.
Traceback (most recent call last):
  File "/home/me/test2.py", line 10, in <module>
    prob.solve(solver=cp.CVXOPT, verbose=True)
  File "/home/me/venv/lib/python3.10/site-packages/cvxpy/problems/problem.py", line 503, in solve
    return solve_func(self, *args, **kwargs)
  File "/home/me/venv/lib/python3.10/site-packages/cvxpy/problems/problem.py", line 1086, in _solve
    self.unpack_results(solution, solving_chain, inverse_data)
  File "/home/me/venv/lib/python3.10/site-packages/cvxpy/problems/problem.py", line 1411, in unpack_results
    raise error.SolverError(
cvxpy.error.SolverError: Solver 'CVXOPT' failed. Try another solver, or solve with verbose=True for more information.

When the same model is run with the default ECOS solver, the correct answer is returned.

Looking through the traceback in cvxpy/problems/problem.py the error is being raised beginning at line 1410 in the problem.py file:

if solution.status in s.ERROR:
            raise error.SolverError(
                    "Solver '%s' failed. " % chain.solver.name() +
                    "Try another solver, or solve with verbose=True for more "
                    "information.")

I am unsure what is causing this, but suspect it is either a syntax issue in the model formulation or a default setting on the CVXOPT solver, but it seems that either documentation is missing, a default setting is insufficient for this use case, or both, and that should be flagged for users in the documentation.

EDIT: adding that the CVXOPT solver works in this environment, for example solving the cvxpy LP example with solver=cp.CVXOPT returns correct answer.

[chofchof]

Your example will be reduced to the following CVXOPT linear cone program.

from cvxopt import matrix, solvers

c = matrix(-1.0, (2, 1))
G = matrix(1.0, (1, 2))
h = matrix(10.0)
solvers.conelp(c, G, h)

However it raises ValueError: Rank(A) < p or Rank([G; A]) < n. Here, $A$ is empty so that the rank of $[G; A]$ is less than $n=2$.

If you replace x = cp.Variable(n) with x = cp.Variable(n, nonneg=True), you will get a result.

-------------------------------------------------------------------------------
                                Numerical solver
-------------------------------------------------------------------------------
(CVXPY) Apr 18 01:59:31 PM: Invoking solver CVXOPT  to obtain a solution.
     pcost       dcost       gap    pres   dres   k/t
 0: -6.6667e+00 -2.0000e+01  1e+01  0e+00  2e-16  1e+00
 1: -8.7325e+00 -1.0100e+01  1e+00  4e-16  1e-16  1e-01
 2: -9.9873e+00 -1.0005e+01  2e-02  1e-16  2e-16  2e-03
 3: -9.9999e+00 -1.0000e+01  2e-04  5e-16  4e-16  2e-05
 4: -1.0000e+01 -1.0000e+01  2e-06  3e-16  3e-16  2e-07
Optimal solution found.
-------------------------------------------------------------------------------
                                    Summary
-------------------------------------------------------------------------------
(CVXPY) Apr 18 01:59:31 PM: Problem status: optimal
(CVXPY) Apr 18 01:59:31 PM: Optimal value: 1.000e+01
(CVXPY) Apr 18 01:59:31 PM: Compilation took 3.182e-03 seconds
(CVXPY) Apr 18 01:59:31 PM: Solver (including time spent in interface) took 2.314e-03 seconds

The optimal value is 9.999998732501222
A solution x is
[4.99999937 4.99999937]
A dual solution is
1.0000000462353087

[GrahamHulsey]

Interesting, thanks for your digging. I believe this issue is essentially a duplicate of #1588 , as reporting the CVXOPT ValueError would be helpful for debugging. I will mark as duplicate

[GrahamHulsey]

Duplicate of #1588