This dissertation deals with the efficient operation of LNG liquefaction plants based on the concept of self-optimizing control. Self-optimizing control is known as a promising alternative to model-based online optimization techniques and gained more and more attention in the scientific and industrial community during the last decade. Among others, the the dynamic modeling of spiral-wound heat exchangers, the synthesis of self-optimizing control structures and the nonlinear steady-state and dynamical verification of self-optimizing control structures are discussed in this work.