Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-06T06:16:41.032Z Has data issue: false hasContentIssue false

Strict feasibility of generalized complementarity problems

Published online by Cambridge University Press:  09 April 2009

Y. R. He
Affiliation:
Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan, P. R., China, e-mail: [email protected]
K. F. Ng
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, e-mail: [email protected]
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.

Type
Research Article
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). 211216.CrossRefGoogle Scholar
[2]Crouzeix, J.-P., ‘Pseudomonotone variational inequality problems: Existence of solutions’, Math. Program. Ser. A 78 (1997). 305314.CrossRefGoogle Scholar
[3]Daniilidis, A. and Hadjisavvas, N., ‘Coercivity conditions and variational inequalities’, Math. Program. Ser. A 86 (1999), 433438.CrossRefGoogle Scholar
[4]He, Y., ‘A relationship between pseudomonotone and monotone mappings’, Appl. Math. Lett. 17 (2004), 459461.CrossRefGoogle Scholar
[5]McLinden, L., ‘Stable monotone variational inequalities’, Math. Program. Ser. B 48 (1990), 303338.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), 260266.CrossRefGoogle Scholar
[9]Sion, M., ‘On general minimax theorems’, Pacific J. Math. 8 (1958), 171176.CrossRefGoogle Scholar