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Nonlinear Elastic-Net Regularization and Its Iterative Soft Thresholding Algorithm
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DOI：10.1515/cmam-2024-0176.png)
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Abstract
En 中文
Elastic-net regularization, as a variational method, demonstrates enhanced stability compared to classical & ell; 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 & ell; 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.
Keywords:
Sparsity Regularization
Elastic-Net Regularization
Nonlinear
Generalized Conditional Gradient Method
Journal
C
IF:
1.2
Papers:
21
Citations:
0