zbMATH — the first resource for mathematics

Optimal solutions to variational inequalities on Banach lattices. (English) Zbl 1231.49011
Summary: We study the existence of maximum and minimum solutions to generalized variational inequalities on Banach lattices. The main tools of analysis are the variational characterization of the generalized metric projection operator and order-theoretic fixed point theory.

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
Full Text: DOI
[1] Alber, Ya., Metric and generalized projection operators in Banach spaces: properties and applications, (), 15-50 · Zbl 0883.47083
[2] Borwein, J.; Dempster, M., The linear order complementarity problem, Math. oper. res., 14, 534-558, (1989) · Zbl 0692.90096
[3] Chitra, A.; Subrahmanyam, P., Remarks on nonlinear complementarity problem, J. optim. theory appl., 53, 297-302, (1987) · Zbl 0595.90089
[4] Fujimoto, T., An extension of tarskiʼs fixed point theorem and its application to isotone complementarity problems, Math. programming, 28, 116-118, (1984) · Zbl 0526.90084
[5] Hartman, P.; Stampacchia, G., On some nonlinear elliptic differential functional equations, Acta math., 115, 153-188, (1966) · Zbl 0142.38102
[6] Isac, G., On the order monotonicity of the metric projection operator, () · Zbl 0848.46008
[7] Li, J., The generalized projection operator on reflexive Banach spaces and its applications, J. math. anal. appl., 306, 55-71, (2005) · Zbl 1129.47043
[8] J. Li, J.-C. Yao, The existence of maximum and minimum solutions to general variational inequalities in Hilbert lattices, J. Fixed Point Theory Appl. (2011), doi:10.1155/2011/904320, forthcoming. · Zbl 1215.49015
[9] Meyer-Nieberg, P., Banach lattices, Universitext, (1991), Springer-Verlag · Zbl 0743.46015
[10] H. Nishimura, E.A. Ok, Solvability of variational inequalities on Hilbert lattices, Math. Oper. Res. (2011), forthcoming. · Zbl 1297.90155
[11] Ok, E.A., Order theory, (2011)
[12] Takahashi, W., Nonlinear functional analysis, (2000), Yokohama Publishers
[13] Topkis, D., Supermodularity and complementarity, (1998), Princeton University Press
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.