I found the CPLEX QP method contains Primal Simplex. Theoretically, Simplex method can’t be use to solve QP method, because The Simplex Method works by iterating through the vertices of the feasible region to optimize a linear objective function. However, quadratic programming problems involve a quadratic objective function. Due to the curvature of quadratic functions, the optimal solution may lie in the interior or on the boundary of the feasible region, not necessarily at a vertex. Thus, the Simplex Method cannot directly handle quadratic objectives. 

So, I wonder if the Primal Simplex could really solve the QP problem, or it can only solve a part of them. Besides, I want to know if there is any hidden danger of using simplex method to solve QP problems.