Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-14T06:28:55.614Z Has data issue: false hasContentIssue false
  • English
  • Français

Strict feasibility of generalized complementarity problems

Part of: Existence theories

Published online by Cambridge University Press:  09 April 2009

Y. R. He  and
K. F. Ng
Y. R. He
Affiliation:
Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan, P. R., China, e-mail: yiranhe@hotmail.com
K. F. Ng
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, e-mail: kfng@math.cuhk.edu.hk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The existence of strictly feasible points is shown to be equivalent to the boundedness of solution sets of generalized complementarity problems with stably pseudomonotone mappings. This generalizes some known results in the literature established for complementarity problems with monotone mappings.

Keywords

generalized complementarity problemstably pseudomonotone mappingstrict feasibilityupper hemicontinuous set-valued mapping.

MSC classification

Secondary: 90C33: Complementarity and equilibrium problems and variational inequalities (finite dimensions) 49J40: Variational methods including variational inequalities
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 1 , August 2006 , pp. 15 - 20
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Chen, B.. Chen, X. and Kanzow, C., ‘A penalized Fischer-Burmeister NCP-function’, Math. Program. Ser. A 88 (2000). 211–216.CrossRefGoogle Scholar
[2]Crouzeix, J.-P., ‘Pseudomonotone variational inequality problems: Existence of solutions’, Math. Program. Ser. A 78 (1997). 305–314.CrossRefGoogle Scholar
[3]Daniilidis, A. and Hadjisavvas, N., ‘Coercivity conditions and variational inequalities’, Math. Program. Ser. A 86 (1999), 433–438.CrossRefGoogle Scholar
[4]He, Y., ‘A relationship between pseudomonotone and monotone mappings’, Appl. Math. Lett. 17 (2004), 459–461.CrossRefGoogle Scholar
[5]McLinden, L., ‘Stable monotone variational inequalities’, Math. Program. Ser. B 48 (1990), 303–338.CrossRefGoogle Scholar
[6]Rockafellar, R. T., Convex analysis (Princeton University Press, Princeton, N.J., 1970).CrossRefGoogle Scholar
[7]Rockafellar, R. T. and Wets, R. J.-B., Variational analysis (Springer, Berlin, 1998).CrossRefGoogle Scholar
[8]Saigal, R., ‘Extension of the generalized complementarity problem’, Math. Oper. Res. 1 (1976), 260–266.CrossRefGoogle Scholar
[9]Sion, M., ‘On general minimax theorems’, Pacific J. Math. 8 (1958), 171–176.CrossRefGoogle Scholar