<p>This paper considers a new version of the forward-backward-forward splitting algorithm to find a zero of the sum of two monotone operators in real Hilbert spaces. Our proposed method comprises a forward-backward-forward algorithm, an inertial term, correction terms, and a self-adaptive stepsize. Under certain standard conditions, we obtain the proposed method’s weak and linear convergence results. Numerical experiments show that our proposed algorithm outperforms other forward-backward-forward splitting algorithms in the literature. Some popular splitting algorithms have also been recovered from our algorithm.</p>

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A New Version of Forward-Backward-Forward Splitting Algorithm For Monotone Inclusions

  • Grace Nnennaya Ogwo,
  • Chinedu Izuchukwu,
  • Yekini Shehu,
  • Xiaopeng Zhao

摘要

This paper considers a new version of the forward-backward-forward splitting algorithm to find a zero of the sum of two monotone operators in real Hilbert spaces. Our proposed method comprises a forward-backward-forward algorithm, an inertial term, correction terms, and a self-adaptive stepsize. Under certain standard conditions, we obtain the proposed method’s weak and linear convergence results. Numerical experiments show that our proposed algorithm outperforms other forward-backward-forward splitting algorithms in the literature. Some popular splitting algorithms have also been recovered from our algorithm.