We develop certified tracking procedures for Newton homotopies, which are homotopies for which only the constant terms are changed. For these homotopies, our certified procedures include using a constant predictor with Newton corrections, an Euler predictor with no corrections, and an Euler predictor with Newton corrections. In each case, the predictor is guaranteed to produce a point in the qu...

We show how the method of pseudo-transient continuation can be applied to improve the robustness of the Newton iteration within a nonlinear transient elasticity simulation. Pseudotransient continuation improves efficiency and robustness of the transient analysis by enabling larger time steps than possible with a Newton iteration. We illustrate the algorithm by reporting on a simulation of a buc...

In this paper we present a hybrid path-following algorithm that generates inexact Newton steps suited for solving large scale and/or degenerate nonlinear programs. The algorithm uses as a central region a relaxed notion of the central path, called quasicentral path, a generalized augmented Lagrangian function, weighted proximity measures, and a linesearch within a trust region strategy. We appl...

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...

In the Newton/log-barriermethod,Newton steps are taken for the log-barrier function for a xed value of the barrier parameter until a certain convergence criterion is satis ed. The barrier parameter is then decreased and the Newton process is repeated. A naive analysis indicates that Newton's method does not exhibit superlinear convergence to the minimizer of each instance of the log-barrier fun...

Large-scale logistic regression arises in many applications such as document classification and natural language processing. In this paper, we apply a trust region Newton method to maximize the log-likelihood of the logistic regression model. The proposed method uses only approximate Newton steps in the beginning, but achieves fast convergence in the end. Experiments show that it is faster than...

Convergence properties are presented for Newton additive and multiplicative Schwarz iterative methods for the solution of nonlinear systems in several variables. These methods consist of approximate solutions of the linear Newton step using either additive or multiplicative Schwarz iterations, where overlap between subdomains can be used. Restricted versions of these methods are also considered...

This paper describes a method of dogleg trust-region steps, or restricted Levenberg-Marquardt steps, based on a projection process onto the Krylov subspaces for neural networks nonlinear least squares problems. In particular, the linear conjugate gradient (CG) method works as the inner iterative algorithm for solving the linearized Gauss-Newton normal equation, whereas the outer nonlinear algor...

We introduce a well-developed Newton iterative (truncated Newton) algorithm for solving large-scale nonlinear systems. The framework is an inexact Newton method globalized by backtracking. Trial steps are obtained using one of several Krylov subspace methods. The algorithm is implemented in a Fortran solver called NITSOL that is robust yet easy to use and provides a number of useful options and...