In this paper it is shown how to efficiently solve an optimal control problem with applications to model predictive control. The objective is quadratic and the constraints can be both linear and quadratic. The key to an efficient implementation is to rewrite the optimization problem as a second order cone program. This can be done in many different ways. However, done carefully, it is possible to use both very efficient scalings as well as Riccati recursions for computing the search directions.

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