Just to weigh in here, if you have access to Gurobi as a solver, then you can solve problems to global optimality provided they are quadratic constraints with the NonConvex settings. In JuMP, this would be set as
Of course, the issue is having cubic / trilinear terms. A reformulation to quadratic / bilinear form is possible, such as rewriting z = x_1 x_2 x_3 as y = x_1 x_2 and z = y x_3.