×

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
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Ames, W. F., Numerical Methods for Partial Differential Equations (1992), Academic Press: Academic Press New York · Zbl 0219.35007
[2] Baiocchi, C.; Capelo, A., Variational and Quasi Variational Inequalities (1984), Wiley: Wiley New York · Zbl 1308.49003
[3] Cottle, R. W.; Giannessi, F.; Lions, J. L., Variational Inequalities and Complementarity Problems: Theory and Applications (1980), Wiley: 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: Plenum New York · Zbl 0834.00044
[6] Glowinski, R.; Lions, J. L.; Trémolières, R., Numerical Analysis of Variational Inequalities (1981), North-Holland: North-Holland Amsterdam · Zbl 0508.65029
[7] Glowinski, R.; Le Tallec, P., Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics (1989), SIAM: 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.; 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.; 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
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.