Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities

@article{Xu2003ConvergenceOH,
  title={Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities},
  author={H. Xu and T. Kim},
  journal={Journal of Optimization Theory and Applications},
  year={2003},
  volume={119},
  pages={185-201}
}
  • H. Xu, T. Kim
  • Published 2003
  • Mathematics
  • Journal of Optimization Theory and Applications
AbstractAssume that F is a nonlinear operator on a real Hilbert space H which is η-strongly monotone and κ-Lipschitzian on a nonempty closed convex subset C of H. Assume also that C is the intersection of the fixed point sets of a finite number of nonexpansive mappings on H. We devise an iterative algorithm which generates a sequence (xn) from an arbitrary initial point x0∈H. The sequence (xn) is shown to converge in norm to the unique solution u* of the variational inequality $$\left\langle… Expand
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