A Riemannian Dimension-Reduced Second-Order Method with Application in Sensor Network Localization

SIAM Journal on Scientific Computing, Volume 46, Issue 3, Page A2025-A2046, June 2024.
Abstract. In this paper, we propose a cubic-regularized Riemannian optimization method (RDRSOM), which partially exploits the second-order information and achieves the iteration complexity of [math]. In order to reduce the per-iteration computational cost, we further propose a practical version of RDRSOM which is an extension of the well-known Barzilai–Borwein method, which enjoys the worst-case iteration complexity of [math]. Moreover, under more stringent conditions, RDRSOM achieves the iteration complexity of [math]. We apply our method to solve a nonlinear formulation of the wireless sensor network localization problem whose feasible set is a Riemannian manifold that has not been considered in the literature before. Numerical experiments are conducted to verify the high efficiency of our algorithm compared to state-of-the-art Riemannian optimization methods and other nonlinear solvers.