Nonlinear Elastic-Net Regularization and Its Iterative Soft Thresholding Algorithm

Abstract Elastic-net regularization, as a variational method, demonstrates enhanced stability compared to classical ℓ 1 {\ell_{1}} sparsity regularization, making it suitable for addressing ill-conditioned problems. However, conventional elastic-net regularization is typically limited to linear equations. In this paper, we extend the elastic-net regularization method to nonlinear problems. We investigate the well-posedness of this regularization and demonstrate that it serves as a sparsity regularization approach. The iterative soft thresholding algorithm, commonly used for classical ℓ 1 {\ell_{1}} sparsity regularization, features a straightforward structure and is easy to implement. We show that, under widely accepted conditions regarding the nonlinearity of the function F, this algorithm is effective in solving the elastic-net regularization for nonlinear ill-conditioned equations. Our numerical results highlight the efficiency of the proposed method.

• Publication year

  2025

• Venue

  Comput. Methods Appl. Math.

• Publication date

  2025-11-10

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1515/cmam-2024-0176
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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