This paper investigates application of SQP optimization algorithm to nonlinear model predictive control. It considers feasible vs. infeasible path methods, sequential vs. simultaneous methods and reduced vs full space methods. A new optimization algorithm coined rFOPT which remains feasibile with respect to inequality constraints is introduced. The suitable choices between these various strategies are assessed informally through a small CSTR case study. The case study also considers the effect various discretization methods have on the optimization problem.