- Sparse Regularization via Bidualization Amir Beck(beckatauex.tau.ac.il) Yehonathan Refael(yonatanrefael100gmail.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 Citation: Download: [PDF]Entry Submitted: 01/07/2020Entry Accepted: 01/07/2020Entry Last Modified: 01/07/2020Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.