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On modified hybrid steepest-descent methods for general variational inequalities. (English) Zbl 1123.49009
A general variational inequalities (GVI) and modified hybrid steepest descent methods for their solving are considered in the paper. Especially an iterative algorithm with variable parameters for their solving is proposed and analyzed. It is shown that the sequence obtained from this algorithm converges in norm to the solution of GVI under some formulated conditions. Applications to constrained generalized pseudo-inverse is included. The results obtained in the paper also hold for variational inequalities, quasi-variational inequalities and complementary problems since they are special cases of general variational inequalities.

MSC:
49J40Variational methods including variational inequalities
49M30Other numerical methods in calculus of variations