A globally trust-region LP-Newton method for nonsmooth functions under the Hölder metric subregularity

We describe and analyse a globally convergent algorithm to find a possible nonisolated zero of a piecewise smooth mapping over a polyhedral set, such formulation includes Karush-Kuhn-Tucker (KKT) systems, variational inequalities problems, and generalized Nash equilibrium problems. Our algorithm is based on a modification of the fast locally convergent Linear Programming (LP)-Newton method with a … Read more

Convergence Conditions for Newton-type Methods Applied to Complementarity Systems with Nonisolated Solutions

We consider a class of Newton-type methods for constrained systems of equations that involve complementarity conditions. In particular, at issue are the constrained Levenberg–Marquardt method and the recently introduced Linear Programming-Newton method, designed for the difficult case when solutions need not be isolated, and the equation mapping need not be differentiable at the solutions. We … Read more

A New Error Bound Result for Generalized Nash Equilibrium Problems and its Algorithmic Application

We present a new algorithm for the solution of Generalized Nash Equilibrium Problems. This hybrid method combines the robustness of a potential reduction algorithm and the local quadratic convergence rate of the LP-Newton method. We base our local convergence theory on an error bound and provide a new sufficient condition for it to hold that … Read more