The representation of a function in a higher-dimensional space, often referred to as lifting, can be used to reduce complexity.
We investigate how lifting affects the convergence properties of Newton-type methods. For the first time, we conduct a systematic comparison of several lifting strategies on a set of 40 optimal control problems. In addition, we consider differences between interior-point and sequential quadratic programming methods, accounting for both Quasi-Newton approximations and exact Hessians. Based on these observations, we propose an adaptive lifting algorithm that reduces the number of iterations by about 27% on average across all problems and by more than 50% for selected problems compared with naïve lifting approaches.