Solver failed error for bilinear terms

[smehdia]

When a bilinear product is used in your example, CVXOPT solver fails:

from numpy.random import randn
import cvxpy as cvx
from qcqp import *
n, m = 10, 15
A = randn(m, n)
b = randn(m, 1)
x = cvx.Variable(n)
obj = cvx.sum_squares(A*x - b)
cons = [cvx.square(x) == 1]
cons.extend([x[0]*x[1] == 1])
prob = cvx.Problem(cvx.Minimize(obj), cons)
qcqp = QCQP(prob)
qcqp.suggest(SDR)
print("SDR lower bound: %.3f" % qcqp.sdr_bound)
f_cd, v_cd = qcqp.improve(COORD_DESCENT)
print("Coordinate descent: objective %.3f, violation %.3f" % (f_cd, v_cd))
print(x.value)

Output:

`  File "/usr/local/lib/python3.6/dist-packages/qcqp/qcqp.py", line 391, in suggest
    self.sdr_sol, self.sdr_bound = solve_sdr(self.qcqp_form, *args, **kwargs)
  File "/usr/local/lib/python3.6/dist-packages/qcqp/qcqp.py", line 92, in solve_sdr
    rel_prob.solve(*args, **kwargs)
  File "/usr/local/lib/python3.6/dist-packages/cvxpy/problems/problem.py", line 209, in solve
    return self._solve(*args, **kwargs)
  File "/usr/local/lib/python3.6/dist-packages/cvxpy/problems/problem.py", line 335, in _solve
    self._update_problem_state(results_dict, sym_data, solver)
  File "/usr/local/lib/python3.6/dist-packages/cvxpy/problems/problem.py", line 447, in _update_problem_state
    "Solver '%s' failed. Try another solver." % solver.name())
cvxpy.error.SolverError: Solver 'CVXOPT' failed. Try another solver.