This paper presents fast algorithms for estimating generalized linear models with convex penalties, including linear regression, logistic regression, and multinomial regression, using cyclical coordinate descent. The algorithms handle large datasets and sparse features efficiently. They are particularly effective for the elastic net penalty, which combines $ \ell_1 $ and $ \ell_2 $ penalties. The methods compute solutions along a regularization path, leveraging warm starts to improve efficiency. The algorithms are implemented in the R package glmnet, which is publicly available. The paper compares the performance of these algorithms with other methods, showing that they are significantly faster, especially for large datasets. The algorithms are applied to both dense and sparse data, and the paper discusses their use in logistic and multinomial regression. The methods are also shown to be effective in real-world applications, such as gene expression data and document classification. The paper concludes that the proposed algorithms are efficient and effective for a wide range of generalized linear models with convex penalties.This paper presents fast algorithms for estimating generalized linear models with convex penalties, including linear regression, logistic regression, and multinomial regression, using cyclical coordinate descent. The algorithms handle large datasets and sparse features efficiently. They are particularly effective for the elastic net penalty, which combines $ \ell_1 $ and $ \ell_2 $ penalties. The methods compute solutions along a regularization path, leveraging warm starts to improve efficiency. The algorithms are implemented in the R package glmnet, which is publicly available. The paper compares the performance of these algorithms with other methods, showing that they are significantly faster, especially for large datasets. The algorithms are applied to both dense and sparse data, and the paper discusses their use in logistic and multinomial regression. The methods are also shown to be effective in real-world applications, such as gene expression data and document classification. The paper concludes that the proposed algorithms are efficient and effective for a wide range of generalized linear models with convex penalties.