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<p>In this paper, we design a new splitting method for solving nonmonotone inclusions in Hilbert spaces. Our method incorporates an inertial term, and a correction term into the forward-backward algorithm. The weak convergence of the sequence of iterations is derived, with worst-case rates of <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>o</mi> <mo stretchy="false">(</mo> <msup> <mi>k</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$o(k^{-1})$</EquationSource> </InlineEquation> in terms of both the discrete velocity and the fixed point residual. The new method recovers the method in the literature as a special case. We also give some numerical experiments to demonstrate the efficiency of the proposed method.</p>

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A Fast Forward-Backward Splitting Method for Nonmonotone Inclusions

  • 期刊论文

  • 发表日期：

    2026年2月11日

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  • Thanh Quoc Trinh,
  • Tuan Anh Pham,
  • Van Dung Nguyen

摘要

In this paper, we design a new splitting method for solving nonmonotone inclusions in Hilbert spaces. Our method incorporates an inertial term, and a correction term into the forward-backward algorithm. The weak convergence of the sequence of iterations is derived, with worst-case rates of o ( k − 1 ) $o(k^{-1})$ in terms of both the discrete velocity and the fixed point residual. The new method recovers the method in the literature as a special case. We also give some numerical experiments to demonstrate the efficiency of the proposed method.