# A Primal Dual Active Set with Continuation Algorithm for the ℓ0-Regularized Optimization Problem

arXiv: https://arxiv.org/abs/1403.0515 · HTML: https://mlsanity.com/paper/1403.0515/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2014.

## Built on by (most cited first, 3 of 3)

- [Solving Elliptic Problems with Singular Sources using Singularity Splitting Deep Ritz Method](https://mlsanity.com/paper/2209.02931/) (2022)
- [A Data-Driven Line Search Rule for Support Recovery in High-dimensional Data Analysis](https://mlsanity.com/paper/2111.10806/) (2021)
- [An adaptive shortest-solution guided decimation approach to sparse high-dimensional linear regression](https://mlsanity.com/paper/2211.15057/) (2022)

## Abstract (arXiv)

We develop a primal dual active set with continuation algorithm for solving the ℓ0-regularized least-squares problem that frequently arises in compressed sensing. The algorithm couples the the primal dual active set method with a continuation strategy on the regularization parameter. At each inner iteration, it first identifies the active set from both primal and dual variables, and then updates the primal variable by solving a (typically small) least-squares problem defined on the active set, from which the dual variable can be updated explicitly. Under certain conditions on the sensing matrix, i.e., mutual incoherence property or restricted isometry property, and the noise level, the finite step global convergence of the algorithm is established. Extensive numerical examples are presented to illustrate the efficiency and accuracy of the algorithm and the convergence analysis.