A Theoretical And Numerical Comparison Of Some Semismooth Algorithms For Complementarity Problems

: 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 search 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. Key Words: Nonlinear complementarity problem, semismoothness, Newton's method, projected gradient method, large-scale problem. AMS Subject Classification: 90C33, 90C06, 65K05. 1 Introduction The main aim of this paper is twofold: On the one hand, we present a general scheme which allows us to easily analyze and compare, in a unified framework, the characteristics of several semismooth algorithms for the solution of the nonlin..