Primal-Dual Affine Scaling Methods for Nonlinear Problems

Abstract

(Monotone) Nonlinear complementarity problems ((M)NCPs) form a large class of mathematical programming problems with many applications. For instance, any convex programming problem can be modeled as an MNCP. This class of problems is closely related to the class of variational inequalities, which play an important role in the study of equilibria in, e.g., economics, transportation planning and game-theory. We refer to Cottle et al. [34] and Pang [198] for surveys on complementarity problems. A survey on variational inequalities is provided by Harker and Pang [98].