Developed speed control-based air conflict avoidance models using MINLP that do not require any form of discretization. We maximize the number of conflicts resolved subject to subliminal speed control constraints. A pre-processing algorithm is presented to reduce the size of the MINLP formulations. A new approach together with a greedy algorithm is proposed to find the largest set of conflict-free aircraft. Results on benchmark instances show that the proposed models and algorithms are efficient and versatile.