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Zbl 0991.49004
Noor, M.A.
Some algorithms for general monotone mixed variational inequalities. (English)
[J] Math. Comput. Modelling 29, No.7, 1-9 (1999). ISSN 0895-7177

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 {\it B. S. He} [Appl. Math. Optimization 35, No. 1, 69-76 (1997; Zbl 0865.90119)], {\it M. V. Solodov} and {\it P. Tseng} [SIAM J. Control Optimization 34, No. 5, 1814-1830 (1996; Zbl 0866.49018)], and {\it 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 2000:: *49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators
65K10 Optimization techniques (numerical methods)
90C33 Complementarity problems

Keywords: iterative methods; monotone mixed variational inequalities; convergence analysis

Citations: Zbl 0865.90119; Zbl 0866.49018; Zbl 0927.49004; Zbl 0941.49005; Zbl 0994.47061

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