A Monotone Semismooth Newton Method for a Kind of Tensor Complementarity Problem

A semismooth Newton method for tensor eigenvalue complementarity problem

In this paper, we consider the tensor eigenvalue complementarity problem which is closely related to the optimality conditions for polynomial optimization, as well as a class of differential inclusions with nonconvex processes. By introducing an NCP-function, we reformulate the tensor eigenvalue complementarity problem as a system of nonlinear equations. We show that this function is strongly s...

A feasible semismooth asymptotically Newton method for mixed complementarity problems

Semismooth Newton methods constitute a major research area for solving mixed complementarity problems (MCPs). Early research on semismooth Newton methods is mainly on infeasible methods. However, some MCPs are not well defined outside the feasible region or the equivalent unconstrained reformulations of other MCPs contain local minimizers outside the feasible region. As both these problems coul...

A least-square semismooth Newton method for the second-order cone complementarity problem

We present a nonlinear least-square formulation for the second-order cone complementarity problem based on the Fischer-Burmeister (FB) function and the plus function. The formulation has twofold advantages. Firstly, the operator involved in the overdetermined system of equations inherits the favorable properties of the FB function for local convergence, for example, the (strong) semismoothness....

Properties of a Class of Ncp-functions and a Related Semismooth Newton Method for Complementarity Problems

In this paper, we aim to explore properties of a class of NCP-functions and investigate a related semismooth Newton method for complementarity problems. Some favorite properties about the class of NCP-functions and its merit function are discussed including strong semismoothness, continuous differentiability and the nonsingularity of the element in C-subdifferential. In particular, we present a...

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