Sequential quadratic programming (SQP) may be very efficient compared with other techniques for the optimization of simple processes for the liquefaction of natural gas (LNG), and can be combined with process evaluation using commercial flowsheet simulators. However, the level of success is dependent on the formulation of the problem. In this work, effects of varying different aspects of the optimization problem formulation is investigated, such as variable selection, formulae for the estimation of derivatives, initial values, variable bounds, and formulation of constraints. Especially the formulation of the constraint for the temperature difference between the hot and cold composite curve is essential. The commonly used minimum temperature difference constraint should generally not be employed in gradient based optimization. Recommendations regarding optimization of simple LNG processes using SQP and flowsheet simulators are provided.