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.
|Number of pages||20|
|Journal||Journal of Global Optimization|
|State||Published - Mar 2022|
- Convex envelope
- Randomized root search