A smoothing Newton-type method for generalized nonlinear complementarity problem

A Truly Globally Convergent Newton-Type Method for the Monotone Nonlinear Complementarity Problem

A Regularized Smoothing Newton Method for Symmetric Cone Complementarity Problems

This paper extends the regularized smoothing Newton method in vector optimization to symmetric cone optimization, which provide a unified framework for dealing with the nonlinear complementarity problem, the second-order cone complementarity problem, and the semidefinite complementarity problem (SCCP). In particular, we study strong semismoothness and Jacobian nonsingularity of the total natura...

A regularized smoothing Newton method for solving the symmetric cone complementarity problem

The symmetric cone complementarity problem (denoted by SCCP) is a class of equilibrium optimization problems, and it contains the standard linear/nonlinear complementarity problem (LCP/NCP), the second-order cone complementarity problem (SOCCP) and the semidefinite complementarity problem (SDCP) as special cases. In this paper, we present a regularized smoothing Newton algorithm for SCCP by mak...

A Regularization Newton Method for Solving Nonlinear Complementarity Problems

In this paper we construct a regularization Newton method for solving the nonlinear complementarity problem (NCP(F)) and analyze its convergence properties under the assumption that F is a P0-function. We prove that every accumulation point of the sequence of iterates is a solution of NCP(F) and that the sequence of iterates is bounded if the solution set of NCP(F) is nonempty and bounded. More...

Smoothing Functions and A Smoothing Newton Method for Complementarity and Variational Inequality Problems

In this paper, we discuss smoothing approximations of nonsmooth functions arising from complementarity and variational inequality problems. We present some new results which are essential in designing Newton-type methods. We introduce several new classes of smoothing functions for nonlinear complementarity problems and order complementarity problems. In particular, in the first time some comput...