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Sparse Regularization via Bidualization

Amir Beck(becka***at***tauex.tau.ac.il)
Yehonathan Refael(yonatanrefael100***at***gmail.com)

Abstract: The paper considers the sparse envelope function, defined as the biconjugate of the sum of a squared $\ell_2$-norm function and the indicator of the set of $k$-sparse vectors. It is shown that both function and proximal values of the sparse envelope function can be reduced into a one-dimensional search that can be efficiently performed in linear time complexity in expectation. For inverse problems, the sparse envelope function naturally serves as a regularizer that can handle both sparsity and grouping information on the vector to be estimated, and the paper is concluded with a numerical example illustrating the potential effectiveness of the approach.

Keywords: sparse regularization; biduality; proximal methods; elastic net; SVM

Category 1: Convex and Nonsmooth Optimization


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Entry Submitted: 01/07/2020
Entry Accepted: 01/07/2020
Entry Last Modified: 01/07/2020

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