Sparse regularization via bidualization

Amir Beck*, Yehonathan Refael

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The paper considers the sparse envelope function, defined as the biconjugate of the sum of a squared ℓ2-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.

Original languageEnglish
Pages (from-to)463-482
Number of pages20
JournalJournal of Global Optimization
Issue number3
StatePublished - Mar 2022


  • Biconjugate
  • Convex envelope
  • Randomized root search
  • Sparsity


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