Abstract
In this paper, we introduce the new concept of α-exceptional families of elements and (α,β)-exceptional families of elements for continuous functions, and utilize these notions for the study of the feasibility of nonlinear complementarity problems in R n and an infinite-dimensional Hilbert space H without the assumption K *⫅ K.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bershchanskii, Y.M. and Meerov, M.V. (1983), The complementarity problem: theory and methods of solution, Auto. Remote Control 44: 687-710.
Cottle, R.W., Pang, J.S. and Stone, R.E. (1992), The Linear Complementarity Problem, Acdemic Press, New York
Kalashnikov, V. (1995), Complementarity problem and the generalized oligopoly model, Habilitation Thesis, Central Economics and Mathematics Institute, Moscow, Russia.
Kojima, M.A. (1975), Unification of the existence theorems of the nonlinear complementarity problem, Math. Program. 9(2): 257-277.
Lloyd, N.G. (1978), Degree Theory, Cambridge Tracts in Mathematics 73: Cambridge University Press.
Megiddo, N. (1977), A monotone complementarity problem with feasible solutions but no complementary solution, Math. Program. Study 12: 131-132.
Mosco, U. (1976), Implicit Variational Problems and Quasi-variational Inequalities, Lecture Notes in Math. 543: Springer, Berlin.
Isac, G., Kostreva, M.M. and Wiecek, M.M. (1995), Multiple-objective approximation of feasible but unsolvable linear complementarity problems, J. Optim. Theory Appl. 86: 389-405.
Isac, G. (2000), Exceptional families of elements, feasibility and complementarity, J. Optim. Theory Appl. 104(3): 577-588.
Isac, G. (2000), Topological Methods in Complementarity Theory, Kluwer Academic Publishers, Dordrecht.
Isac, G. and Obuchowska, W.T. (1998), Functions without EFE and complementarity problems, J. Optim. Theory Appl. 99(1): 147-163.
Isac, G., Bulavski, V. and Kalashnikov, V. (1997), Exceptional families, topological degree and complementarity problems, J. Global Optim. 10: 207-225.
Zhao, Y.B., Han, J.Y. and Qi, H.D. (1999), Exeptional families and existence theorems for variational inequality problems, J. Optim. Theory Appl. 101(2): 475-495.
Zhao, Y.B. and Han, J.Y. (1999), Exeptional family of elements for a variational inequality problem and its applications, J. Global Optim. 14: 313-330.
Zhang, L.P., Han, J.Y. and Xu, D.C. (2000), The existence of solutions for variational inequalities, Science in China, 30(10):, 893-899.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Huang, Nj., Gao, Cj. & Huang, Xp. Exceptional Family of Elements and Feasibility for Nonlinear Complementarity Problems. Journal of Global Optimization 25, 337–344 (2003). https://doi.org/10.1023/A:1022410913734
Issue Date:
DOI: https://doi.org/10.1023/A:1022410913734