In this paper we present a new algorithm for the solution of nonlinear complementarity problems. The algorithm is based on a semismooth equation re-formulation of the complementarity problem. We exploit the recent extension of Newton's method to semismooth systems of equations and the fact that the natural merit function associated to the equation reformulation is continuously diieren-tiable to...

A complementarity problem with a continuous mapping f from R n into itself can be written as the system of equations F(x, y ) = 0 and ( x , y ) > 0. Here F is the mapping from R ~ " into itself defined by F(x, y) = ( x l y ,, x 2 y Z , . . . , x , ~ y e , y f f x ) ) . Under the assumption that the mapping f is a P,,-function, we study various aspects of homotopy continuation methods that trace...

A continuous function f with domain X and range f(X) in R n is weakly univalent if there is a sequence of continuous one-to-one functions on X converging to f uniformly on bounded subsets of X. In this article, we establish, under certain conditions, the connectedness of an inverse image f ?1 (q). The univalence results of Radulescu-Radulescu, Mor e-Rheinboldt, and Gale-Nikaido follow from our ...

Recently Tseng (Math Program 83:159–185, 1998) extended a class of merit functions, proposed by Luo and Tseng (A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the Art, pp. 204–225, 1997), for the nonlinear complementarity problem (NCP) to the semidefinite complementarity problem (SDCP) and showed several related pro...

We study the continuous trajectories for solving monotone nonlinear mixed complementarity problems over symmetric cones. While the analysis in [5] depends on the optimization theory of convex log-barrier functions, our approach is based on the paper of Monteiro and Pang [17], where a vast set of conclusions concerning continuous trajectories is shown for monotone complementarity problems over t...

This paper introduces two concepts of exceptional families for a class of nonlinear projection equations which provide a uniied formulation of nite-dimensional variational inequalities and complementarity problems. Based on these concepts, two alternative theorems are established for this class of nonlinear projection equations. We utilize one of the alternative theorems to establish several ne...

In this paper, we consider a new formulation with recourse for a class of stochastic nonlinear complementarity problems. We show that the new formulation is equivalent to a smooth semi-infinite program that no longer contains recourse variables. We then propose a combined Monte Carlo sampling and penalty method for solving the problem in which the underlying sample space is assumed to be compac...