In this work we propose a class of quasi-Newton methods to minimize a twice differentiable function with Lipschitz continuous Hessian. These methods are based on the quadratic regularization of Newton’s method, with algebraic explicit rules for computing the regularizing parameter. The...

We give a framework for the globalization of a nonsmooth Newton method. In part one we start with recalling B. Kummer’s approach to convergence analysis of a nonsmooth Newton method and state his results for local convergence. In part two we give a globalized version of this method. Our...

We give a framework for the globalization of a nonsmooth Newton method. In part one we start with recalling B. Kummer’s approach to convergence analysis of a nonsmooth Newton method and state his results for local convergence. In part two we give a globalized version of this method. Our...