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A Scale Invariant Approach for Sparse Signal Recovery
In this paper, we study the ratio of the $L_1 $ and $L_2 $ norms, denoted as $L_1/L_2$, to promote sparsity.
On the exact recovery of sparse signals via conic relaxations
We focus on the cardinality constrained formulation, and prove that the relaxation proposed by Dong, etc.
Regularization vs. Relaxation: A conic optimization perspective of statistical variable selection
In particular, we show that a popular sparsity-inducing concave penalty function known as the Minimax Concave Penalty (MCP), and the reverse Huber penalty derived in a recent work by Pilanci, Wainwright and Ghaoui, can both be derived as special cases of a lifted convex relaxation called the perspective relaxation.
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