Unified Framework of Extragradient-Type Methods for Pseudomonotone Variational Inequalities

Y. J. Wang, N. H. Xiu and C. Y. Wang
Additional contact information
Y. J. Wang: Institute of Operations Research
N. H. Xiu: Northern Jiaotong University
C. Y. Wang: Qufu Normal University

Journal of Optimization Theory and Applications, 2001, vol. 111, issue 3, No 8, 656 pages

Abstract: Abstract In this paper, we propose a unified framework of extragradient-type methods for solving pseudomonotone variational inequalities, which allows one to take different stepsize rules and requires the computation of only two projections at each iteration. It is shown that the modified extragradient method of Ref. 1 falls within this framework with a short stepsize and so does the method of Ref. 2 with a long stepsize. It is further demonstrated that the algorithmic framework is globally convergent under mild assumptions and is sublinearly convergent if in addition a projection-type error bound holds locally. Preliminary numerical experiments are reported.

Keywords: Variational inequalities; extragradient-type method; pseudomonotonicity; unified framework; convergence (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (5)

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DOI: 10.1023/A:1012606212823

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