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

Authors
Citation
Hd. Qi, On minimizing and stationary sequences of a new class of merit functions for nonlinear complementarity problems, J OPTIM TH, 102(2), 1999, pp. 411-431
Citations number
22
Categorie Soggetti
Engineering Mathematics
Journal title
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
ISSN journal
00223239 → ACNP
Volume
102
Issue
2
Year of publication
1999
Pages
411 - 431
Database
ISI
SICI code
0022-3239(199908)102:2<411:OMASSO>2.0.ZU;2-0
Abstract
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.