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The forward–backward splitting method for non-Lipschitz continuous minimization problems in Banach spaces

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Abstract

In this paper we propose the forward–backward splitting methods with linesearches for solving nonsmooth optimization problems without the standard assumption of the Lipschitz continuity of the gradient in Banach spaces. We prove the weak convergence of the iterative sequence generated by these methods, and further prove convergence with asymptotic rate \(\frac{1}{n}\) to the optimal value under the assumption of the boundedness of the iterative sequence.

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Acknowledgements

The work was supported by PHD research startup foundation of Harbin Normal University(No. XKB201804) and the National Natural Sciences Grant(No. 11871182)

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  1. School of Mathematical Sciences, Harbin Normal University, Harbin, 150025, People’s Republic of China

    Wei-Bo Guan & Wen Song

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  1. Wei-Bo Guan
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  2. Wen Song
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Correspondence to Wen Song.

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Guan, WB., Song, W. The forward–backward splitting method for non-Lipschitz continuous minimization problems in Banach spaces. Optim Lett 16, 2435–2456 (2022). https://doi.org/10.1007/s11590-021-01840-y

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