— Computing the Newton step for a generic function f : R N → R takes O(N 3) flops. In this paper, we explore avenues for reducing this bound, when the computational structure of f is known beforehand. It is shown that the Newton step can be computed in time, linear in the size of the computational-graph, and cubic in its tree-width.
— In this paper we describe a new algorithm for the trajectory optimization of mechanical systems. Our method incorporates pseudospectral methods for function approximation with variational discretization schemes that exactly preserve conserved mechanical quantities. We use pseudospectral methods to obtain a global discretization of the Lagrange-d'Alembert… (More)