CVXOPT with CVXPY fails to solve simple linear prorgam

[Graham Hulsey]

Hello,

I have installed cvxopt and cvxpy in a virtual environment on my Linux machine, running Ubuntu 22.04.4 LTS. I installed both packages through pip.

I took the cvxpy LP example problem and set the solver to cp.CVXOPT, and got the correct solution, which tells me that the packages are working. Then, I wrote the following extremely simple LP:

import cvxpy as cp
import numpy as np

n = 2
x = cp.Variable(n)

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

which solves correctly with the ECOS solver. However, when I take the above model and set solver=cp.CVXOPT, the model fails. The output of the solver is here:

===============================================================================
                                     CVXPY                                    
                                     v1.4.3                                    
===============================================================================
(CVXPY) Apr 17 08:55:08 PM: Your problem has 2 variables, 1 constraints, and 0 parameters.
(CVXPY) Apr 17 08:55:08 PM: It is compliant with the following grammars: DCP, DQCP
(CVXPY) Apr 17 08:55:08 PM: (If you need to solve this problem multiple times, but with different data, consider using parameters.)
(CVXPY) Apr 17 08:55:08 PM: CVXPY will first compile your problem; then, it will invoke a numerical solver to obtain a solution.
(CVXPY) Apr 17 08:55:08 PM: Your problem is compiled with the CPP canonicalization backend.
-------------------------------------------------------------------------------
                                  Compilation                                  
-------------------------------------------------------------------------------
(CVXPY) Apr 17 08:55:08 PM: Compiling problem (target solver=CVXOPT).
(CVXPY) Apr 17 08:55:08 PM: Reduction chain: FlipObjective -> Dcp2Cone -> CvxAttr2Constr -> ConeMatrixStuffing -> CVXOPT
(CVXPY) Apr 17 08:55:08 PM: Applying reduction FlipObjective
(CVXPY) Apr 17 08:55:08 PM: Applying reduction Dcp2Cone
(CVXPY) Apr 17 08:55:08 PM: Applying reduction CvxAttr2Constr
(CVXPY) Apr 17 08:55:08 PM: Applying reduction ConeMatrixStuffing
(CVXPY) Apr 17 08:55:08 PM: Applying reduction CVXOPT
(CVXPY) Apr 17 08:55:08 PM: Finished problem compilation (took 2.663e-03 seconds).
-------------------------------------------------------------------------------
                                Numerical solver                              
-------------------------------------------------------------------------------
(CVXPY) Apr 17 08:55:08 PM: Invoking solver CVXOPT  to obtain a solution.
Traceback (most recent call last):
  File "/home/graham/test2.py", line 8, in <module>
    prob.solve(solver=cp.CVXOPT, verbose=True)
  File "/home/graham/venv/lib/python3.10/site-packages/cvxpy/problems/problem.py", line 503, in solve
    return solve_func(self, *args, **kwargs)
  File "/home/graham/venv/lib/python3.10/site-packages/cvxpy/problems/problem.py", line 1086, in _solve
    self.unpack_results(solution, solving_chain, inverse_data)
  File "/home/graham/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.

I am unable to determine why CVXOPT cannot solve this problem, but think it may be related to the syntax of the constraints. Any help is much appreciated.

[Martin]

The dual to the problem that you are solving has redundant constraints, which means that the problem that cvxpy is passing to cvxopt does not satisfy a certain rank requirement (see https://cvxopt.org/userguide/coneprog.html#linear-cone-programs).

You can either reformulate the problem (e.g., replace sum(x) by a scalar variable) or you can try the following:

   prob.solve(solver="CVXOPT", kktsolver="robust")