\min_A \|D - DA\|_F^2 + \lambda \|A\|_{2,1}Explain the admm optimization problem with the help of a toy and it is used for Extractive Summarization Using ℓ₂,₁ Regularization

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We introduce an optimization problem for extractive summarization using ADMM. The objective function minimizes the Frobenius norm of reconstruction error D minus DA, plus lambda times the L2,1 norm of matrix A. Here D represents the document matrix containing sentence features, A is the selection matrix that determines which sentences to include, and lambda controls the trade-off between reconstruction accuracy and sparsity.