DOI: 10.24193/fpt-ro.2020.2.57

Authors: Liling Wei and Hong-Kun Xu

Abstract: The p-elastic net (p-EN) with 1 < p < ∞ is introduced to recover a sparse signal x ∈ ℝⁿ from m (< n) linear measurements with noise. The p-EN, which extends the elastic net of Zou and Hastie [23] and was implicitly suggested by Tropp [16], amounts to minimizing the objective function over x ∈ ℝⁿ, where A is the measurement matrix, b is the observation, and λ > 0, μ > 0 are regularization parameters. Some basic geometric properties of the p-EN such as how the solution curve of the minimization depends on the parameters λ and μ are investigated. Moreover, iterative algorithms such as the proximal-gradient algorithm and the Frank-Wolfe algorithm are studied for solving the p-EN.

Key Words and Phrases: Lasso, compressed sensing, elastic net, 𝓁_p-norm error, proximal gradient, Frank-Wolfe.

2010 Mathematics Subject Classification: 49J20, 47J06, 47J25, 47H10, 49N45.

Published on-line: July 1st, 2020.

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