Convergence analysis of modified hybrid steepest-descent methods with variable parameters for variational inequalities

Lu-Chuan Zeng Ngai-Ching Wong Jen-Chih Yao

Functional Analysis mathscidoc:1910.43628

Journal of Optimization Theory and Applications, 132, (1), 51-69, 2007.1
Assume that <i>F</i> is a nonlinear operator on a real Hilbert space <i>H</i> which is -strongly monotone and -Lipschitzian on a nonempty closed convex subset <i>C</i> of <i>H</i>. Assume also that <i>C</i> is the intersection of the fixed-point sets of a finite number of nonexpansive mappings on <i>H</i>. We construct an iterative algorithm with variable parameters which generates a sequence {<i>x</i> <sub> <i>n</i> </sub>} from an arbitrary initial point <i>x</i> <sub>0</sub> <i>H</i>. The sequence {<i>x</i> <sub> <i>n</i> </sub>} is shown to converge in norm to the unique solution <i>u</i> <sup></sup> of the variational inequality
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@inproceedings{lu-chuan2007convergence,
  title={Convergence analysis of modified hybrid steepest-descent methods with variable parameters for variational inequalities},
  author={Lu-Chuan Zeng, Ngai-Ching Wong, and Jen-Chih Yao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020204731887354157},
  booktitle={Journal of Optimization Theory and Applications},
  volume={132},
  number={1},
  pages={51-69},
  year={2007},
}
Lu-Chuan Zeng, Ngai-Ching Wong, and Jen-Chih Yao. Convergence analysis of modified hybrid steepest-descent methods with variable parameters for variational inequalities. 2007. Vol. 132. In Journal of Optimization Theory and Applications. pp.51-69. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020204731887354157.
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