Newton map in optimization
= Newton map in optimization
{c}
{title2=$N(p)=p-H(p)^{-1}\nabla f(p)$}
For a twice continuously differentiable real <function>, the Newton map sends an input $p$ to the next iterate of <Newton's method in optimization>. It is defined where the <Hessian matrix> $H(p)$ is invertible. Iterating this map seeks a <zero of a function> of the <gradient>; additional information is needed to determine whether a resulting <stationary point> is a <local minimum>.