Optimal decision-making tools are essential in industry to achieve high performance. One of these tools is model predictive control (MPC), which is an advanced control technique that generates an action that affects the controlled variables, while satisfying the process’ operational constraints. At the core of the MPC algorithm lies an optimization problem that is solved by a numerical method at every sample time. New demand for more self-contained modular processes has seen MPC embedded in small-scale platforms. This has prompted a need for custom-made numerical methods that help to run the computationally demanding optimization algorithms efficiently. In this paper, we propose two approaches that factorize the Newton system of the interior-point method based on the two-point boundary-value problem structure, rarely explored in MPC. By exploiting the Hamiltonian form of the augmented system, we derive an incomplete LU factorization. A direct method is available to compute the solution of the system using a forward substitution of a series of matrices. We also propose a preconditioned Krylov method that converges within a small number of iterations only depending on the number of states.