A Theoretical and Numerical Comparison of Some Semismooth Algorithms for Complementarity Problems

Abstract

In this paper we introduce a general line search scheme which easily allows us to define and analyze known and new semismooth algorithms for the solution of nonlinear complementarity problems. We enucleate the basic assumptions that a reach direction to be used in the general scheme has to enjoy in order to guarantee global convergence, local superlinear/quadratic convergence or finite convergence. We examine in detail several different semismooth algorithms and compare their theoretical features and their practical behavior on a set of large-scale problems.