The main objective of this work presented in the paper is to perform an optimization of the stator nozzle. This is done using a 1D two-phase metastable model which includes a transitional interface area formulation, the Aleksandrov interface heat transfer coefficient and Schiller-Naumann interface drag model. The optimization is based on the research of an optimal pressure profile defined by Bezier curves leading to an optimal cross-sectional area profile. Various types of linear constrained optimization algorithms were explored. The results show that for inlet operating conditions close to critical point of CO2, the maximum efficiency that can be attained is always higher than at lower inlet temperature conditions. The obtained optimal nozzle profiles should be tested in subsequent experimental work in order to evaluate the performance of the method.