Forward-Backward Splitting Method with Viscosity Iteration for Solving Monotone Inclusion Problems

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@article{1704279,
      author = {Francis O Nwawuru, Grace N Echezona},
      title = {Forward-Backward Splitting Method with Viscosity Iteration for Solving Monotone Inclusion Problems},
      journal = {Iconic Research And Engineering Journals},
      year = {2023},
      volume = {6},
      number = {10},
      pages = {588-594},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1704279.pdf},
      abstract = {In this paper, we introduce and study a modified forward-backward splitting method for finding a zero inthe sum of two monotone operators in real Hilbert spaces. Our proposed method only requires one forward evaluation of the single-valued operator and onebackward evaluation of the set-valued operator per iteration. This is an improvement over many others in literature with strongly convergent splitting methods with two forwards and a backward iteration. Furthermore, we also incorporate inertial term in our scheme to speed up the rate of convergence. We obtain a strong convergence result when the set-valued operator is maximal monotoneand the single-valued operator is Lipschitz continuous monotone which is weaker assumption than being inverse strongly monotone or cocoercive.},
      keywords = {viscosity iteration method; Inertial method; Inclusion problem; Maximal monotone operator; Forward?backward algorithm.},
      month = {April},
  }