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Complexity Bounds of Iterative Linear Quadratic Optimization Algorithms for Discrete Time Nonlinear Control
A classical approach for solving discrete time nonlinear control on a finite
horizon consists in repeatedly minimizing linear quadratic approximations of
the original problem around current candidate solutions. While widely popular
in many domains, such an approach has mainly been analyzed locally. We observe
that global convergence guarantees can be ensured provided that the linearized
discrete time dynamics are surjective and costs on the state variables are
strongly convex. We present how the surjectivity of the linearized dynamics can
be ensured by appropriate discretization schemes given the existence of a
feedback linearization scheme. We present complexity bounds of algorithms based
on linear quadratic approximations through the lens of generalized Gauss-Newton
methods. Our analysis uncovers several convergence phases for regularized
generalized Gauss-Newton algorithms