It is known that complementarity functions play an important role in dealing with complementarity problems. The most well known complementarity problem is the symmetric cone complementarity problem (SCCP) which includes nonlinear complementarity problem (NCP), semidefinite complementarity problem (SDCP), and second-order cone complementarity problem (SOCCP) as special cases. Moreover, there is ...

We consider the Tikhonov regularization method for the second-order cone complementarity problem (SOCCP) with the Cartesian P0-property. We show that many results of the regularization method for the P0 nonlinear complementarity problem still hold for this important class of nonmonotone SOCCP. For example, under the more general setting, every regularized problem has a unique optimal solution, ...

A reformulation of the mixed complementarity problem as a box constrained overdetermined system of semismooth equations or, equivalently, a box constrained nonlinear least squares problem with zero residual is presented. Based on this reformulation, a trust region method for the solution of mixed complementarity problems is considered. This trust region method contains elements from different a...

Variational inequality theory besides being elegant, exciting and rich, also provides us a unified and natural framework to study a large class of linear and nonlinear problems arising in mathematical and engineering sciences. Equally important is the area of operations research known as complementarity theory, which has received much attention during the last twenty years. It has been shown by...

This paper develops complementarity constraints for nonlinear feedback control systems with additive output disturbances and sensor noise, and for nonlin-ear ltering in the presence of process noise and additive measurement noise. In the control case, the complementarity constraint is the nonlinear counterpart of the well known fact in linear feedback control theory that the sum of the sensitiv...

Regularization methods for the solution of nonlinear complementarity problems are standard methods for the solution of monotone complementarity problems and possess strong convergence properties. In this paper, we replace the monotonicity assumption by a P0-function condition. We show that many properties of regularization methods still hold for this larger class of problems. However, we also p...