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Li, Jinlu; Yao, Jen-Chih

The existence of maximum and minimum solutions to general variational inequalities in the Hilbert lattices. (English) Zbl 1215.49015

Fixed Point Theory Appl. 2011, Article ID 904320, 19 p. (2011).
Summary: We apply the variational characterization of the metric projection to prove some results about the solvability of general variational inequalities and the existence of maximum and minimum solutions to some general variational inequalities in the Hilbert lattices.

Cited in 7 Documents

MSC:

49J40 Variational inequalities

Keywords:

variational characterization; general variational inequalities; Hilbert lattices
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\textit{J. Li} and \textit{J.-C. Yao}, Fixed Point Theory Appl. 2011, Article ID 904320, 19 p. (2011; Zbl 1215.49015)
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References:

[1] Cottle RW, Pang JS: A least-element theory of solving linear complementarity problems as linear programs.Mathematics of Operations Research 1978,3(2):155-170. 10.1287/moor.3.2.155 · Zbl 0385.90077
[2] Cryer CW, Dempster MAH: Equivalence of linear complementarity problems and linear programs in vector lattice Hilbert spaces.SIAM Journal on Control and Optimization 1980,18(1):76-90. 10.1137/0318005 · Zbl 0428.90077
[3] Cryer CW, Dempster MAH: Equivalence of linear complementarity problems and linear programs in vector lattice Hilbert spaces.SIAM Journal on Control and Optimization 1980,18(1):76-90. 10.1137/0318005 · Zbl 0428.90077
[4] Isac G: Complementarity Problems, Lecture Notes in Mathematics. Volume 1528. Springer, Berlin, UK; 1992:vi+297. · Zbl 0795.90072
[5] Isac G, Li J: Complementarity problems, Karamardian’s condition and a generalization of Harker-Pang condition.Nonlinear Analysis Forum 2001,6(2):383-390. · Zbl 1002.90073
[6] Isac G, Sehgal VM, Singh SP: An alternate version of a variational inequality.Indian Journal of Mathematics 1999,41(1):25-31. · Zbl 1034.49005
[7] Nishimura H, Ok EA: Solvability of variational inequalities on Hilbert lattices. to appear · Zbl 1297.90155
[8] Park S: Generalized equilibrium problems and generalized complementarity problems.Journal of Optimization Theory and Applications 1997,95(2):409-417. 10.1023/A:1022643407038 · Zbl 0892.90173
[9] Topkis DM: Supermodularity and Complementarity, Frontiers of Economic Research. Princeton University Press, Princeton, NJ, USA; 1998:xii+272.
[10] Yao JC, Guo J-S: Variational and generalized variational inequalities with discontinuous mappings.Journal of Mathematical Analysis and Applications 1994,182(2):371-392. 10.1006/jmaa.1994.1092 · Zbl 0809.49005
[11] Zhang CJ: Generalized variational inequalities and generalized quasi-variational inequalities.Applied Mathematics and Mechanics 1993,14(4):315-325. · Zbl 0780.49010
[12] Zhang, C-J, Existence of solutions of two abstract variational inequalities, 153-161 (2001), Huntington, NY, USA · Zbl 1073.49506
[13] Borwein JM, Dempster MAH: The linear order complementarity problem.Mathematics of Operations Research 1989,14(3):534-558. 10.1287/moor.14.3.534 · Zbl 0692.90096
[14] Borwein JM, Yost DT: Absolute norms on vector lattices.Proceedings of the Edinburgh Mathematical Society II 1984,27(2):215-222. · Zbl 0589.46005
[15] Smithson RE: Fixed points of order preserving multifunctions.Proceedings of the American Mathematical Society 1971,28(1):304-310. 10.1090/S0002-9939-1971-0274349-1 · Zbl 0238.06003
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