Weak Convergence of an Iterative Method for Pseudomonotone Variational Inequalities and Fixed-Point Problems

Weak Convergence of an Iterative Method for Pseudomonotone Variational Inequalities and Fixed-Point Problems

We consider an iterative scheme for finding a common element of the set of solutions of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of N nonexpansive mappings. The proposed iterative method combines two well-known schemes: extragradient an...

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Veröffentlicht in:Journal of optimization theory and applications 2010-07, Vol.146 (1), p.19-31
Hauptverfasser: Ceng, L. C., Teboulle, M., Yao, J. C.
Format: Artikel
Sprache:eng
Schlagworte:
Academic disciplines
Applications of Mathematics
Applied mathematics
Applied sciences
Calculus of variations and optimal control
Calculus of Variations and Optimal Control
Optimization
Engineering
Exact sciences and technology
Hilbert space
Inequality
Iterative methods
Mapping
Mathematical analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Operational research and scientific management
Operational research. Management science
Operations Research/Decision Theory
Optimization
Sciences and techniques of general use
Studies
Theory of Computation
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Zusammenfassung:We consider an iterative scheme for finding a common element of the set of solutions of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of N nonexpansive mappings. The proposed iterative method combines two well-known schemes: extragradient and approximate proximal methods. We derive a necessary and sufficient condition for weak convergence of the sequences generated by the proposed scheme.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-010-9650-0