Sparse regularization via bidualization

Amir Beck () and Yehonathan Refael ()
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Amir Beck: Tel Aviv University
Yehonathan Refael: Tel Aviv University

Journal of Global Optimization, 2022, vol. 82, issue 3, No 2, 463-482

Abstract: Abstract The paper considers the sparse envelope function, defined as the biconjugate of the sum of a squared $$\ell _2$$ ℓ 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. The sparse envelope function naturally serves as a regularizer that can handle both sparsity and grouping information in inverse problems, and can also be utilized in sparse support vector machine problems.

Keywords: Biconjugate; Sparsity; Convex envelope; Randomized root search (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-021-01089-w

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