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

  • Authors:

  • Yair Censor;Aviv Gibali;Simeon Reich

  • Affiliations:

  • Department of Mathematics, University of Haifa, Haifa, Israel;Department of Mathematics, The Technion - Israel Institute of Technology, Haifa, Israel;Department of Mathematics, The Technion - Israel Institute of Technology, Haifa, Israel

  • Venue:
  • Optimization Methods & Software - Advances in Shape and Topology Optimization: Theory, Numerics and New Applications Areas
  • Year:
  • 2011

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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.