A NEW MERIT FUNCTION FOR NONLINEAR COMPLEMENTARITY-PROBLEMS AND A RELATED ALGORITHM

We investigate the properties of a new merit function which allows us to reduce a nonlinear complementarity problem to an unconstrained glob al minimization one. Assuming that the complementarity problem is defi ned by a P-0-function, we prove that every stationary point of the unc onstrained problem is a global solution; furthermore, if the complemen tarity problem is defined by a uniform P-function, the level sets of t he merit function are bounded. The properties of the new merit functio n are compared with those of Mangasarian-Solodov's implicit Lagrangian and Fukushima's regularized gap function. We also introduce a new sim ple active-set local method for the solution of complementarity proble ms and show how this local algorithm can be made globally convergent b y using the new merit function.