Properties and splitting method for the p-Elastic Net

Journal Article

Xu, • N. Altwaijry, S. Chebbi, and H.K. . 2015

• المجلة \ الصحيفة: Pacific Journal of Optimization

مستخلص المنشور

The lasso of Tibshirani is a popular model for variable selections.
The elastic net of Zou and Hastie applies Tikhonov's regularization to the
lasso to break some limitations of the lasso in the case where the number of
predictors is much bigger than the number of observations, or where a group
of variables have pairwise high correlations. We generalize the elastic net by
replacing Tikhonov's regularization with a more general `p-norm regularization
which we refer to as the p-elastic net. One diculty for dealing with the p-
elastic net lies in the fact that the `p-norm raised to the pth power fails to
have a Lipschitz continuous gradient. We will discuss fundamental properties
of the p-elastic net, and moreover, provide a splitting proximal algorithm for
solving the p-elastic net.