For unconstrained optimization, Newton-type methods have good convergence properties, and areused in practice. The Newton’s method combined with a trust-region method (the TR-Newtonmethod), the cubic regularization of Newton’s method and the regularized Newton method withline search methods are such Newton-type methods. The TR-Newton method and the cubic regu-larization of N...

We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is c...

Quasi-Newton methods are widely used in practise for convex loss minimization problems. These methods exhibit good empirical performance on a wide variety of tasks and enjoy super-linear convergence to the optimal solution. For largescale learning problems, stochastic Quasi-Newton methods have been recently proposed. However, these typically only achieve sub-linear convergence rates and have no...

A new nonlinear solution method is developed and applied to a non-equilibrium radiation di!usion problem. With this new method, Newton-like super-linear convergence is achieved in the nonlinear iteration, without the complexity of forming or inverting the Jacobian from a standard Newton method. The method is a unique combination of an outer Newton-based iteration and and inner conjugate gradien...

Recently, Roos proposed a full-Newton step infeasible interiorpoint method (IIPM) for solving linear optimization (LO) problems. Later on, more variants of this algorithm were published. However, each main step of these methods is composed of one feasibility step and several centering steps. The purpose of this paper is to prove that by using a new search direction it is enough to take only one...

Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes b...

The purpose of this work was to investigate the utility of implicit integration methods for molecular dynamics (MD) simulation. Implicit methods were investigated in an attempt to address the bottleneck associated with short, stability-limited step size lengths available to the explicit methods currently in widespread use. Two implicit methods were compared to the current standard for time inte...

In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity and global convergence result of Kleinman also hold for the inexact Newton iterates. Numerical results ...

This paper analyzes local convergence rates of primal-dual interior point methods for general nonlinearly constrained optimization problems. For this purpose, we first discuss modified Newton methods and modified quasi-Newton methods for solving a nonlinear system of equations, and show local and Qquadratic/Q-superlinear convergence of these methods. These methods are characterized by a perturb...

The R package sns implements Stochastic Newton Sampler (SNS), a Metropolis-Hastings Monte Carlo Markov Chain algorithm where the proposal density function is a multivariate Gaussian based on a local, second-order Taylor-series expansion of log-density. The mean of the proposal function is the full Newton step in Newton-Raphson optimization algorithm. Taking advantage of the local, multivariate ...