Title: Numerical Methods for Solving Nonlinear Complementarity Problems

Nonlinear complementarity problems (NCPs) arise in various fields of mathematics, natural sciences, engineering and economics. For example, we can think of Karush-Kuhn-Tucker conditions of nonlinear programs, discretized obstacle problems, the Wardrop principle for transportation networks, or Walrasian equilibrium models. Therefore, there is a growing interest in efficient and robust numerical methods for NCPs that are large or highly nonlinear.

We will review several theoretical approaches for solving NCPs that make use of Newton's linearization principle. Moreover, we will briefly describe corresponding numerical methods and report on existing software.

A second part of the talk will concentrate on one of the most popular approaches for solving NCPs. It is based on the reformulation of the NCP as a semismooth system of equations by means of so-called NCP-functions. In particular, we will report on properties and the numerical behavior of a Newton-type algorithm for solving such systems within the GAMS modeling environment.