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Zbl 1086.49005
Noor, Muhammad Aslam
Projection-proximal methods for general variational inequalities. (English)
[J] J. Math. Anal. Appl. 318, No. 1, 53-62 (2006); with errata. ISSN 0022-247X

Summary: We consider and analyze some new projection-proximal methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is a weaker condition than monotonicity. The proposed methods include several new and known methods as special cases. Our results can be considered as a novel and important extension of the previously known results. Since the general variational inequalities include the quasi-variational inequalities and implicit complementarity problems as special cases, results proved in this paper continue to hold for these problems.

MSC 2000:: *49J40 Variational methods including variational inequalities
90C33 Complementarity problems
47J20 Inequalities involving nonlinear operators

Keywords: variational inequalities; projection methods; pseudomonotone operators; fixed-point; convergence

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Zentralblatt MATH Berlin [Germany]