Generalized Strongly Nonlinear Quasi-Complementarity Problems in Hilbert Spaces

Zhang Shi-sheng; Huang Nan-jing

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Article Navigation > Applied Mathematics and Mechanics > 1990 > 11(6): 483-488

Zhang Shi-sheng, Huang Nan-jing. Generalized Strongly Nonlinear Quasi-Complementarity Problems in Hilbert Spaces[J]. Applied Mathematics and Mechanics, 1990, 11(6): 483-488.

Citation:

Zhang Shi-sheng, Huang Nan-jing. Generalized Strongly Nonlinear Quasi-Complementarity Problems in Hilbert Spaces[J]. Applied Mathematics and Mechanics, 1990, 11(6): 483-488.

Citation:

Zhang Shi-sheng, Huang Nan-jing. Generalized Strongly Nonlinear Quasi-Complementarity Problems in Hilbert Spaces[J]. Applied Mathematics and Mechanics, 1990, 11(6): 483-488.

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Generalized Strongly Nonlinear Quasi-Complementarity Problems in Hilbert Spaces

Department of Mathematics, Sichuan University, Chengdu

Received Date: 1989-06-17
Publish Date: 1990-06-15

Abstract

Abstract

In this paper, we introduce a new kind of generalized strongly nonlinear quasi-complementarity problems in Hilbert space and discuss the existence of solutions for this kind of problems and the convergence of sequences generated by algorithms. The results presented in this paper improve and extend a number of known results.

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References(17)

References

[1]	Lemke,C.E.,Bimatrix equilibrium points and mathematical programming,Management Sci.,11(1965),681-689.
[2]	Cottle,R.W.and G.B.Dantzig,Complementarity pivot theory of mathematical programming,Linear Algebra Appl.,1(1968),103-125.
[3]	Lin,Y.and C.W.Cryer,An alternating direction implicit algorithm for the solution of linear complementarity problems arising from boundary problems,A ppl.Math.Optim.,13(1985),1-17.
[4]	Cottle,R.W.,Complementarity and variational problems,Sympos.Math.,19(1976),177-208.
[5]	Crank,J.,Free and Moving Boundary Problems,Oxford Univ.Press,London(1984).
[6]	Pang,J.S.,On the convergence of a basic iterative method for the implicit complementarity problems,J.Optim.Theory Appl.,37(1982),149-162.
[7]	Pang,J.S.,The Implicit Complementarity Problem in Nonlinear Programming 4,Ed by O.L.Mangasarian,R.Meyer and S.M.Robinson,Academic Press,New York/London(1981),47-518.
[8]	Noor,M.A.,Generalized quasi-complementarity problem,J.Math.Anal.Appl.,120(1980),321-327.
[9]	Noor,M.A.,Iterative method for quasi-complementarity problems,Methods Oper.Res.,56(1986),75-83.
[10]	Noor,M.A.,The quasi-complementarity problem,J.Math.Anal.Appl.,130(1988),344-353.
[11]	Noor,M.A.and S.Zarae,Linear quasi-complementarity problems,Utilitas Math.,27(1985),249-260.
[12]	Noor,M.A.,On the nonlinear complementarity problem,J.Math.A nal.A ppl.,123(1987),455-460.
[13]	Noor,M.A.,Iterative methods for a class of complementarity problems,J.Math.Anal Appl.,133(1988),366-382.
[14]	Noor,M.A.,Fixed point approach for complementarity problems,J.Math.Anal.App.,133(1988),437-448.
[15]	Noor,M.A.,On variational inequalities,Ph.D.Thesis,Brunei Univ.U.K.(1975).
[16]	Noor,M.A.,An iterative scheme for a class of quasi variational inequalities,J.Math.Anal.Appl.,110(1985),463-468.
[17]	Nalder,S.B.,Jr.,Multi-valued contraction mappings,Pacific J.Math.,30(1969),475-488.