Papers › Semismooth Newton Algorithm for Efficient Projections onto ℓ_(1, ∞)-norm Ball
Semismooth Newton Algorithm for Efficient Projections onto ℓ_(1, ∞)-norm Ball
Dejun Chu, Chang-Shui Zhang, Shiliang Sun, Qing Tao
Structured sparsity-inducing ℓ_(1, ∞)-norm, as a generalization of the classical ℓ₁-norm, plays an important role in jointly sparse models which select or remove simultaneously all the variables forming a group. However, its resulting problem is more difficult to solve than the conventional ℓ₁-norm constrained problem. In this paper, we propose an efficient algorithm for Euclidean projection onto ℓ_(1, ∞)-norm ball. We tackle the projection problem via semismooth Newton algorithm to solve the system of semismooth equations. Meanwhile, exploiting the structure of Jacobian matrix via LU decomposition yields an equivalent algorithm which is proved to terminate after a finite number of iterations. Empirical studies demonstrate that our proposed algorithm outperforms the existing state-of-the-art solver and is promising for the optimization of learning problems with ℓ_(1, ∞)-norm ball constraint.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections