On Choosing Initial Values of Iteratively Reweighted ${\ell }_1$ Algorithms for the Piece-wise Exponential Penalty

Rongrong Lin, Shimin Li, Yulan Liu

Computing the proximal operator of the sparsity-promoting piece-wise exponential (PiE) penalty $1-e^{-|x|/\sigma }$ with a given shape parameter $\sigma >0$, which is treated as a popular nonc…