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New approximation schemes for general variational inequalities. (English) Zbl 0964.49007
Summary: We suggest and consider a class of new three-step approximation schemes for general variational inequalities. Our results include Ishikawa and Mann iterations as special cases. We also study the convergence criteria of these schemes.

MSC:
49J40 Variational inequalities
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[1] Ames, W.F, Numerical methods for partial differential equations, (1992), Academic Press New York · Zbl 0219.35007
[2] Baiocchi, C; Capelo, A, Variational and quasi variational inequalities, (1984), Wiley New York
[3] Cottle, R.W; Giannessi, F; Lions, J.L, Variational inequalities and complementarity problems: theory and applications, (1980), Wiley New York
[4] Douglas, J; Rachford, H.H, On the numerical solution of the heat conduction problem in 2 and 3 space variables, Trans. amer. math. soc., 82, 421-435, (1956) · Zbl 0070.35401
[5] Giannessi, F; Maugeri, A, Variational inequalities and network equilibrium problems, (1995), Plenum New York · Zbl 0834.00044
[6] Glowinski, R; Lions, J.L; Trémolières, R, Numerical analysis of variational inequalities, (1981), North-Holland Amsterdam · Zbl 0508.65029
[7] Glowinski, R; Le Tallec, P, Augmented Lagrangian and operator splitting methods in nonlinear mechanics, (1989), SIAM Philadelphia · Zbl 0698.73001
[8] Haubruge, S; Nguyen, V.H; Strodiot, J.J, Convergence analysis and applications of the glowinski-le tallec splitting method for finding a zero of the sum of two maximal monotone operators, J. optim. theory appl., 97, 645-673, (1998) · Zbl 0908.90209
[9] M. Aslam, Noor, Projection-splitting algorithms for general monotone variational inequalities, J. Comput. Anal. Appl, in press. · Zbl 1039.49010
[10] Noor, M.Aslam, General variational inequalities, Appl. math. lett., 1, 119-121, (1988) · Zbl 0655.49005
[11] Noor, M.Aslam, Wiener – hopf equations and variational inequalities, J. optim. theory appl., 79, 197-206, (1993) · Zbl 0799.49010
[12] M. Aslam, Noor, A predictor-corrector method for general variational inequalities, Appl. Math. Lett, in press.
[13] Noor, M.Aslam, Some iterative techniques for general monotone variational inequalities, Optimization, 46, 391-401, (1999) · Zbl 0966.49010
[14] Noor, M.Aslam, Projection-splitting algorithms for monotone variational inequalities, Comput. math. appl., 39, 73-79, (2000) · Zbl 0948.49002
[15] Noor, M.Aslam, Some algorithms for general monotone mixed variational inequalities, Math. comput. modelling, 29, 1-9, (1999) · Zbl 0991.49004
[16] Noor, M.Aslam, Some recent advances in variational inequalities. part I. basic concepts, New Zealand J. math., 26, 53-80, (1997) · Zbl 0886.49004
[17] Noor, M.Aslam, Some recent advances in variational inequalities. part II. other concepts, New Zealand J. math., 26, 229-255, (1997) · Zbl 0889.49006
[18] Peaceman, D.H; Rachford, H.H, The numerical solution of parabolic elliptic differential equations, SIAM J. appl. math., 3, 28-41, (1955) · Zbl 0067.35801
[19] Tseng, P, A modified forward-backward splitting method for maximal monotone mappings, SIAM J. control optim., 38, 431-446, (2000) · Zbl 0997.90062
[20] Youness, E.A, E-convex sets, E-convex functions and E-convex programming, J. optim. theory appl., 102, 439-450, (1999) · Zbl 0937.90082
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