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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:
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
65K10Optimization techniques (numerical methods)
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)