On Model Selection Consistency of the Elastic Net When p >> n

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Learning Credible Models (2017, neutral): “ridge (1)2 ∥θ ∥2 2 no yes yes elastic net β ∥θ ∥1 + (1)2 (1 − β)∥θ ∥2 2 yes yes conditioned [14] OWL ∑n i=1wi |θ |[i] yes yes unknown weighted LASSO ∥w ⊙ θ ∥1 yes yes no”
Sparse Estimation with Strongly Correlated Variables using Ordered Weighted L1 Regularization (2014, background): “For example, Jia and Yu [14] study the elastic net regularizer (a combination of the `1 and the squared `2 norms), showing that it can consistently select the true model for certain correlated design matrices A, when LASSO cannot.”
The Smooth-Lasso and other ℓ1+ℓ2-penalized methods (2011, methodology): “In the next section, we introduce the estimator ˆ β Quad deﬁned with the Lasso penalty together with a quadratic penalty.”
Identifying a Minimal Class of Models for High-dimensional Data (2015, unknown): “For p > n , it turns out that strong conditions are needed to achieve (6) for popular regularization based estimators such as the Lasso: Zhao & Yu (2006) and Meinshausen & B¨uhlmann (2006); the Adaptive Lasso: Huang, Ma & Zhang (2008); the Elastic Net: Jia & Yu (2010), but also for Orthogonal Matchi”