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Iterative resolvent methods for general mixed variational inequalities. (English) Zbl 1049.49010

Summary: In this paper, we use the technique of updating the solution to suggest and analyze a class of new self-adaptive splitting methods for solving general mixed variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Proof of convergence is very simple. Since general mixed variational inequalities include variational inequalities and complementarity problems as special cases, our results continue to hold for these problems.

MSC:

49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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