% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/newton_step.R
\name{try_newton_step}
\alias{try_newton_step}
\title{Try Newton Step}
\usage{
try_newton_step(g, H)
}
\arguments{
\item{g}{Gradient vector (length n)}

\item{H}{Hessian matrix (n x n symmetric matrix)}
}
\value{
List with components:
\item{success}{Logical; TRUE if Newton step computed successfully}
\item{s}{Newton step vector if successful, NULL otherwise}
\item{pred_reduction}{Predicted reduction from quadratic model if successful, NULL otherwise}
}
\description{
Attempts to compute and validate a Newton step when the Hessian is positive
definite. Uses Cholesky factorization to check positive definiteness and
solve the Newton system.
}
\details{
The algorithm:
\enumerate{
\item Attempts Cholesky factorization of H (fails if H is indefinite)
\item If successful, solves H * s = -g for Newton step
\item Computes predicted reduction from quadratic model
}

No pre-filtering based on sigma is required - the ratio test in the main
ARC loop naturally determines whether Newton steps are appropriate. See
the design notes in \verb{literature/consensus_reviews/} for the rationale
behind not imposing an explicit sigma threshold on the Newton step.
}
\keyword{internal}
