NONLINEAR COMPLEMENTARITY AS UNCONSTRAINED OPTIMIZATION

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