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Some algorithms for general monotone mixed variational inequalities. (English) Zbl 0991.49004

Summary: We consider some new iterative methods for solving general monotone mixed variational inequalities by using the updating technique of the solution. The convergence analysis of these new methods is considered and the proof of convergence is very simple. These new methods are versatile and are easy to implement. Our results differ from those of B. S. He [Appl. Math. Optimization 35, No. 1, 69-76 (1997; Zbl 0865.90119)], M. V. Solodov and P. Tseng [SIAM J. Control Optimization 34, No. 5, 1814-1830 (1996; Zbl 0866.49018)], and M. A. Noor [J. Math. Anal. Appl. 229, No. 1, 330-343 (1999; Zbl 0927.49004); Appl. Math. Lett. 11, No. 4, 109-113 (1998; Zbl 0941.49005); Math. Comput. Modelling 29, No. 3, 95-100 (1999; Zbl 0994.47061)] for solving monotone variational inequalities.

MSC:

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
65K10 Numerical optimization and variational techniques
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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