Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space

Author: Censor Yair   Gibali Aviv   Reich Simeon  

Publisher: Taylor & Francis Ltd

ISSN: 1055-6788

Source: Optimization Methods and Software, Vol.26, Iss.4-5, 2011-10, pp. : 827-845

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Abstract

We study two projection algorithms for solving the variational inequality problem in Hilbert space. One algorithm is a modified subgradient extragradient method in which an additional projection onto the intersection of two half-spaces is employed. Another algorithm is based on the shrinking projection method. We establish strong convergence theorems for both algorithms.