A descent algorithm for generalized complementarity problems based on generalized Fischer-Burmeister functions

We study an unconstrained minimization approach to the generalized complementarity problem GCP( f , g ) based on the generalized Fischer-Burmeister function and its generalizations when the underlying functions are C 1 . Also, we show how, under appropriate regularity conditions, minimizing the merit function corresponding to f and g leads to a solution of the generalized complementarity problem. Moreover, we propose a descent algorithm for GCP( f , g ) and show a result on the global convergence of a descent algorithm for solving generalized complementarity problem. Finally, we present some preliminary numerical results. Our results further give a unified/generalization treatment of such results for the nonlinear complementarity problem based on generalized Fischer-Burmeister function and its generalizations.