Unconstrained optimization reformulation of the generalized nonlinear complementarity problem and related method

In this article, we first propose an unconstrained optimization reformulation of the generalized nonlinear complementarity problem (GNCP) over a polyhedral cone, and then discuss the conditions under which its any stationary point is a solution of the GNCP. The conditions which guarantee the nonsingularity and positive definiteness of the Hessian matrix of the objective function are also given. In the end, we design a Newton-type method to solve the GNCP and show the global and local quadratic convergence of the proposed method under certain assumptions.