×

An implicit method for mixed variational inequalities. (English) Zbl 0941.49005

Summary: We suggest and analyze a new implicit method for solving mixed monotone variational inequalities. This method can be viewed as an extension of He’s method [B. He: “A class of new methods for monotone variational inequalities”, Report, Inst. Math. Nanjing Univ. (1995), per bibl.] for solving monotone variational inequalities.

MSC:

49J40 Variational inequalities
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] He, B., A class of new methods for monotone variational inequalities, (Report (1995), Institute of Mathematics, Nanjing University: Institute of Mathematics, Nanjing University Nanjing, P.R. China)
[2] Baiocchi, C.; Capelo, A., Variational and Quasi-Variational Inequalities (1984), J. Wiley and Sons: J. Wiley and Sons New York · Zbl 1308.49002
[3] Brezis, H., Operateurs Maximaux Monotone et Semigroupes de Contractions dans les Espaces de Hilbert (1973), North-Holland: North-Holland Amsterdam · Zbl 0252.47055
[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, 421-439 (1956) · Zbl 0070.35401
[5] Giannessi, F.; Maugeri, A., Variational Inequalities and Network Equilibrium Problems (1995), Plenum Press: Plenum Press New York · Zbl 0834.00044
[6] Glowinski, R.; Lions, J. L.; Tremolieres, R., Numerical Analysis of Variational Inequalities (1981), North-Holland: North-Holland Amsterdam · Zbl 0508.65029
[7] Noor, M. A., Theory of variational inequalities, (Lecture Notes (1996), Mathematics Department, King Saud University: Mathematics Department, King Saud University Riyadh, Saudi Arabia) · Zbl 0859.49009
[8] Noor, M. A., Some recent advances in variational inequalities, Part I. Basic concepts, New Zealand J. Math., 26, 2, 53-80 (1997) · Zbl 0886.49004
[9] Noor, M. A., Some recent advances in variational inequalities, Part II, Other concepts, New Zealand J. Math., 26, 4, 229-255 (1997) · Zbl 0889.49006
[10] Noor, M. A., Resolvent equations and variational inclusions, J. Nat. Geometry (1998) · Zbl 0912.49012
[11] Noor, M. A.; Noor, K. I., Multivalued variational inequalities and resolvent equations, Mathl. Comput. Modelling, 26, 7, 109-121 (1997) · Zbl 0893.49005
[12] Noor, M. A.; Noor, K. I.; Rassias, Th. M., Some aspects of variational inequalities, J. Comput. Appl. Math., 47, 285-312 (1993) · Zbl 0788.65074
[13] Stampacchia, G., Formes bilineaires coercitives sur les ensembles convexes, C.R. Acad. Sci. Paris, 258, 4413-4416 (1964) · Zbl 0124.06401
[14] He, B., A class of projection and contraction methods for monotone variational inequalities, Applied Math. Optimization, 35, 69-76 (1997) · Zbl 0865.90119
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.