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Simple examples for the failure of Newton's method with line search for strictly convex minimization

Florian Jarre(jarre***at***hhu.de)
Philippe L. Toint(philippe.toint***at***unamur.be)

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 search converges to a point where the gradient of $f$ is 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.

Keywords: nonlinear optimization, convergence Newton's method

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Report naXys-11-2014, Namur Centre for Complex Systems, University of Namur, Belgium

Download: [PDF]

Entry Submitted: 11/11/2014
Entry Accepted: 11/11/2014
Entry Last Modified: 11/11/2014

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