Inexact Newton-Type Optimization with Iterated Sensitivities

Inexact Newton-type Optimization with Iterated

This paper presents and analyzes an Inexact Newton-type optimization method 4 based on Iterated Sensitivities (INIS). A particular class of Nonlinear Programming (NLP) problems 5 is considered, where a subset of the variables is defined by nonlinear equality constraints. The pro6 posed algorithm considers any problem-specific approximation for the Jacobian of these constraints. 7 Unlike other i...

An inexact Newton method for nonconvex equality constrained optimization

We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351–369, 2008]. For nonconvex problems, the methodology developed in this paper allows for the presence o...

Exact and Inexact Subsampled Newton Methods for Optimization

The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how to coordinate the accuracy in the gradient and Hessian to yield a superlinear rate of convergence in expectation. The second part of the paper analyzes an in...

Accelerated Inexact Newton

Inexact Newton Dogleg Methods

The dogleg method is a classical trust-region technique for globalizing Newton’s method. While it is widely used in optimization, including large-scale optimization via truncatedNewton approaches, its implementation in general inexact Newton methods for systems of nonlinear equations can be problematic. In this paper, we first outline a very general dogleg method suitable for the general inexac...