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This paper presents a novel, computationally feasible procedure for computing optimal switching surfaces, i.e. optimal feedback controllers for switched autonomous nonlinear systems. Such systems are regulated by appropriately scheduling their operation modes over time. Given a finite mode sequence, the control task is to determine switching surfaces, which implicitly encode locally optimal switching times for a family of trajectories emerging from a pre-specified initial state set. Optimality of the switching times is assessed according to a nonlinear performance criterion.