# How to use Warm-Start QAOA in QisKit to solve non-convex QUBO problem?

I have a non-convex QUBO problem that I'd like to solve by warm-starting QAOA with a solution obtained from a continuous relaxation solution obtained by a classical algorithm. The specifics of the problem is shown below in the code.

I have 2 questions:

• In the code below is CPLEX able to solve the original QUBO. However, when I use CPLEX as input to the WarmStartQAOA optimization in QisKit, it tells me it cannot solve because the problem is non-convex?
• For non-convex problems, there must be an easy reformulation that QisKit and WarmStartQAOA can do on its own since most problems are non-convex. Can someone help me find that functionality in QisKit?
import random
random.seed(0)

def invert_counts(counts):
return {k[::-1]:v for k, v in counts.items()}

p = 1
m = 4
n = 4
for i in range(m):
for j in range(n):
qp.binary_var("x_{}_{}".format(i,j))

for i in range(m):
for p in range(n):
for i_2 in range(m):
for p_2 in range(n):
for i in range(m):
for p in range(n):
x_i_p = "x_{}_{}".format(i,p)

"""Change all variables to continuous."""
relaxed_problem = copy.deepcopy(problem)
for variable in relaxed_problem.variables:
variable.vartype = VarType.CONTINUOUS
return relaxed_problem

sol = CplexOptimizer().solve(qp)
print(sol.prettyprint())

qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA())
ws_qaoa = WarmStartQAOAOptimizer(
pre_solver=CplexOptimizer(), relax_for_pre_solver=True, qaoa=qaoa_mes, epsilon=0.0)

ws_result = ws_qaoa.solve(qp)
print(ws_result.prettyprint())
$$$$
`
• Did you figure out what was the issue? I get a similar problem. Jun 29 at 16:10