Structural and stability properties of P-0 nonlinear complementarity problems

Authors
Citation
F. Facchinei, Structural and stability properties of P-0 nonlinear complementarity problems, MATH OPER R, 23(3), 1998, pp. 735-745
Citations number
30
Categorie Soggetti
Mathematics
Journal title
MATHEMATICS OF OPERATIONS RESEARCH
ISSN journal
0364765X → ACNP
Volume
23
Issue
3
Year of publication
1998
Pages
735 - 745
Database
ISI
SICI code
0364-765X(199808)23:3<735:SASPOP>2.0.ZU;2-T
Abstract
We consider P-0 nonlinear complementarity problems and study the connectedn ess and stability of the solutions by applying degree theory and the Mounta in Pass Theorem to a smooth reformulation of the complementarity problem. W e show that the solution set is connected and bounded if a bounded isolated component of the solution set exists and that a solution is locally unique if and only if it is globally unique. Furthermore, we prove that a solutio n is stable in Ha's sense if and only if it is globally unique, while the c omplementarity problem is stable if and only if the solution set is bounded .