We propose a fully distributed Newton-type algorithm for state estimation of electric power systems. At each Newton iteration, matrix-splitting techniques are utilized to carry out the matrix inversion for calculating the Newton step in a distributed fashion. In order to reduce the communication burden as well as increase robustness of state estimation, the proposed distributed scheme relies on...

In this paper, we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators and efficient integration of the Schr¨odinger equation. The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant lit...

In this paper we describe a variant of the Inexact Newton method for solving nonlinear systems of equations. We define a nonmonotone Inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone Inexact Newton scheme we present the convergence theorems. Finally, we show how we can apply these strategies to Inexact Newton Interior–Point method and we present some numerical ex...

This paper considers the connection between the intrinsic Riemannian Newton method and other more classically inspired optimization algorithms for equality-constrained optimization problems. We consider the feasibly-projected sequential quadratic programming (FP-SQP) method and show that it yields the same update step as the Riemannian Newton, subject to a minor assumption on the choice of mult...

Computing the Newton step for a generic function f : R → R takes O(N) 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.

Model Predictive Control (MPC) is increasing in popularity in industry as more e cient algorithms for solving the related optimization problem are developed. The main computational bottle-neck in on-line MPC is often the computation of the search step direction, i.e. the Newton step, which is often done using generic sparsity exploiting algorithms or Riccati recursions. However, as parallel har...