Nonlinear complementarity as unconstrained optimization

Several methods for solving the nonlinear complementarity problem (NCP) are developed. These methods are generalizations of the recently proposed algorithm of Mangasarian and Solodov (Ref. 1) and are based on an unconstrained minimization formulation of the nonlinear complementarity problem. It is shown that, under certain assumptions, any stationary point of the unconstrained objective function is already a solution of NCP. In particular, these assumptions are satisfied by the Mangasarian and Solodov implicit Lagrangian function. Furthermore, a special Newton-type method is suggested, and conditions for its local quadratic convergence are given. Finally, some preliminary numerical results are presented.