In this contribution we present two interior-point path-following algo- rithms that solve the convex optimisation problem that arises in recentred barrier function model predictive control (MPC), which includes standard MPC as a lim- iting case. However the optimisation problem that arises in nonlinear MPC may not be convex. In this case we propose sequential convex programming (SCP) as an alternative to sequential quadratic programming. The algorithms are appropriate for the convex program that arises at each iteration of such an SCP.