On minimizing and stationary sequences of a new class of merit functions for nonlinear complementarity problems

Motivated by the work of Fukushima and Pang (Ref. 1), we study the equivale nt relationship between minimizing and stationary sequences of a new class of merit functions for nonlinear complementarity problems (NCP). These meri t functions generalize that obtained via the squared Fischer-Burmeister NCP function, which was used in Ref. 1. We show that a stationary sequence {x( k)}subset of R-n is a minimizing sequence under the condition that the func tion value sequence {F(X-k)} is bounded above or the Jacobian matrix sequen ce {F'(x(k))} is bounded, where F is the function involved in NCP. The latt er condition is also assumed by Fukushima and Pang. The converse is true un der the assumption of {F'(x(k))} bounded. As an example shows, even for a b ounded function F, the boundedness of the sequence {F'(x(k))} is necessary for a minimizing sequence to be a stationary sequence.