An adaptive damped Newton method for strongly monotone and Lipschitz continuous operator equations

Abstract

We will consider the damped Newton method for strongly monotone and Lipschitz continuous operator equations in a variational setting. We will provide a very accessible justification why the undamped Newton method performs better than its damped counterparts in a vicinity of a solution. Moreover, in the given setting, an adaptive step-size strategy will be presented, which guarantees the global convergence and favours an undamped update if admissible.