The expander is one of the key components of an ORC as the cycle efficiency strongly depends on the expander efficiency. This paper presents a method for design optimization of a radial inflow turbine (RIT) using a mean-line model. The novelty of this work lies in the equation-based formulation of the mathematical problem, which enables the use of an efficient gradient based method for optimization. This means that there is no distinction between real decision variables such as specific speed and velocity ratio, and parameters that are unknown a priori such as rotor outlet entropy and velocity. Constraints are imposed to ensure conservation of mass, and to ensure a feasible and consistent design, and the objective is to maximize the total-to-static efficiency. The main results showed an average CPU time less than one second and a success rate of 80% for converging to the global optimum when the independent variables were given random start values. We therefore recommend the proposed method for preliminary RIT-design or to be integrated into an ORC system design model enabling for instance working fluid screening with fluid-dependent expander efficiency.