Projected Reflected Gradient Methods for Monotone Variational Inequalities

@article{Malitsky2015ProjectedRG,
  title={Projected Reflected Gradient Methods for Monotone Variational Inequalities},
  author={Yura Malitsky},
  journal={SIAM J. Optim.},
  year={2015},
  volume={25},
  pages={502-520}
}
  • Yura Malitsky
  • Published 17 February 2015
  • Mathematics, Computer Science
  • SIAM J. Optim.
This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a constant stepsize. It is similar to the projected gradient method, namely, the method requires only one projection onto the feasible set and only one value of the mapping per iteration. This distinguishes our method from most other projection-type methods for… 

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