Simple examples for the failure of Newton's method
with line search for strictly convex minimization
Florian Jarre and Philippe L. Toint
naXys Report NTR-11-2014 November 2014
Abstract.
In this paper two simple examples of a twice continuously differentiable
strictly convex function f are presented for which Newton's method with line
searchconverges to a point where the gradient of fis not zero. The first
example uses a line search based on the Wolfe conditions. For the second
example, some strictly convex function f is defined as well as a sequence of
descent directions for which exact line searches do not converge to the
minimizer of f. Then f is perturbed such that these search directions coincide
with the Newton directions for the perturbed function while leaving the exact
line search invariant.