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Minimization over the $$\ell _1$$ ℓ 1 -ball using an active-set non-monotone projected gradient

Andrea Cristofari (), Marianna Santis (), Stefano Lucidi () and Francesco Rinaldi ()
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Andrea Cristofari: Università degli Studi di Roma “Tor Vergata”
Marianna Santis: Sapienza Università di Roma
Stefano Lucidi: Sapienza Università di Roma
Francesco Rinaldi: Università di Padova

Computational Optimization and Applications, 2022, vol. 83, issue 2, No 10, 693-721

Abstract: Abstract The $$\ell _1$$ ℓ 1 -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 $$\ell _1$$ ℓ 1 -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.

Keywords: Active-set methods; $$\ell _1$$ ℓ 1 -ball; LASSO; Large-scale optimization (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-022-00407-6

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