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Mathematics > Optimization and Control

arXiv:2108.00237 (math)
[Submitted on 31 Jul 2021 (v1), last revised 7 Apr 2022 (this version, v2)]

Title:Minimization over the l1-ball using an active-set non-monotone projected gradient

Authors:Andrea Cristofari, Marianna De Santis, Stefano Lucidi, Francesco Rinaldi
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Abstract:The l1-ball is a nicely structured feasible set that is widely used in many fields (e.g., machine learning, statistics and signal analysis) to enforce some sparsity in the model solutions. In this paper, we devise an active-set strategy for efficiently dealing with minimization problems over the l1-ball and embed it into a tailored algorithmic scheme that makes use of a non-monotone first-order approach to explore the given subspace at each iteration. We prove global convergence to stationary points. Finally, we report numerical experiments, on two different classes of instances, showing the effectiveness of the algorithm.
Comments: 28 pages, 2 figures
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:2108.00237 [math.OC]
  (or arXiv:2108.00237v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2108.00237

Submission history

From: Marianna De Santis [view email]
[v1] Sat, 31 Jul 2021 13:31:35 UTC (234 KB)
[v2] Thu, 7 Apr 2022 11:46:35 UTC (235 KB)
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