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Fixed point approach for complementarity problems. (English) Zbl 0649.65037

The author proposes a change of variables leading to a fixed point formulation of a nonlinear complementary problem. This is useful in the description of general integral methods for solving such solving such problems. Sufficient conditions for the convergence of the iterations are given.
Reviewer: S.Grzegórski

MSC:

65K05 Numerical mathematical programming methods
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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[1] Lemke, C. E., Bimatrix equilibrium points, and mathematical programming, Management Sci., 11, 681-689 (1965) · Zbl 0139.13103
[2] Cottle, R. W.; Dantzig, G. B., Complementarity pivot theory of mathematical programming, Linear Algebra Appl., 1, 103-125 (1968) · Zbl 0155.28403
[3] Crank, J., Free and Moving Boundary Problems (1984), Oxford Univ. Press (Clarendon): Oxford Univ. Press (Clarendon) London · Zbl 0547.35001
[4] Cottle, R. W., Complementarity and variational problems, (Sympos. Math., 19 (1976)), 177-208
[5] Lin, Y.; Cryer, C. W., An alternating direction implicit algorithm for the solution of linear complementarity problems arising from free boundary problems, Appl. Math. Optim., 13, 1-17 (1985) · Zbl 0575.65119
[6] M. Aslam Noor; M. Aslam Noor
[7] Mangasarian, O. L., Solution of symmetric linear complementarity problems by iterative methods, J. Optim. Theory Appl., 22, 465-485 (1977) · Zbl 0341.65049
[8] Ahn, B. H., Solution of nonsymmetric linear complementarity problems by iterative methods, J. Optim. Theory Appl., 33, 175-185 (1981) · Zbl 0422.90079
[9] Ahn, B. H., Iterative methods for linear complementarity problems with upper bounds on primary variables, Math. Programming, 26, 295-315 (1983) · Zbl 0506.90081
[10] Pang, J. S., On the convergence of a basic iterative method for the implicit complementarity problem, J. Optim. Theory Appl., 37, 149-162 (1982) · Zbl 0482.90084
[11] Aganagic, M., Newton’s method for linear complementarity problems, Math. Programming, 28, 349-362 (1984) · Zbl 0533.90088
[12] Karamardian, S., Generalized complementarity problem, J. Optim. Theory Appl., 8, 161-168 (1971) · Zbl 0218.90052
[13] Fang, S., An iterative method for generalized complementarity problems, IEEE Trans. Automat. Control, 25, 1225-1227 (1980) · Zbl 0483.49027
[14] Noor, M. Aslam, Generalized nonlinear complementarity problems, J. Natur. Sci. Math., 26, 9-21 (1986) · Zbl 0595.90088
[15] Van Bokhoven, W. M., A Class of Linear Complementarity Problem Is Solvable in Polynomial Time, (Tech. Rep. (1980), Department of Electrical Engineering, Technical University: Department of Electrical Engineering, Technical University Eindhoven, Holland) · Zbl 0448.65047
[16] Noor, M. Aslam; Zarae, S., An iterative scheme for complementarity problems, Engrg. Anal. J., 3, 240-243 (1986)
[17] Varga, R. S., Matrix Iterative Analysis (1962), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0133.08602
[18] Noor, M. Aslam; Zarae, S., Linear quasi complementarity problems, Utilitas Math., 27, 249-260 (1985) · Zbl 0588.90087
[19] Ortega, J. M.; Rheinboldt, W. C., Iterative Solutions of Nonlinear Equations in Several Variables (1970), Academic Press: Academic Press New York/London · Zbl 0241.65046
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