GROWTH-BEHAVIOR OF A CLASS OF MERIT FUNCTIONS FOR THE NONLINEAR COMPLEMENTARITY-PROBLEM

When the nonlinear complementarity problem is reformulated as that of finding the zero of a self-mapping, the norm of the self-mapping serve s naturally as a merit function for the problem. We study the growth b ehavior of such a merit function. Tn particular, we show that, for the linear complementarity problem, whether the merit function is coerciv e is intimately related to whether the underlying matrix is a P-matrix or a nondegenerate matrix or an R(0)-matrix. We also show that, for t he more popular choices of the merit function, the merit function is b ounded below by the norm of the natural residual raised to a positive integral power. Thus, if the norm of the natural residual has positive order of growth, then so does the merit function.