  We present the online Newton's method, a single-step second-order method for
online nonconvex optimization. We analyze its performance and obtain a dynamic
regret bound that is linear in the cumulative variation between round optima.
We show that if the variation between round optima is limited, the method leads
to a constant regret bound. In the general case, the online Newton's method
outperforms online convex optimization algorithms for convex functions and
performs similarly to a specialized algorithm for strongly convex functions. We
simulate the performance of the online Newton's method on a nonlinear,
nonconvex moving target localization example and find that it outperforms a
first-order approach.

Optimization and Control