DOI: 10.24193/fpt-ro.2023.2.13

Authors: Guohui Liu and Hong-Kun Xu

Abstract: We will study primal-dual fixed point methods for the least-squares problem regularized by l_p-norms with p ∈ [1,2]. Our methods and results extend some of Ribeiro and Richtarik [9] and Silva, et al [10] where the case of p=2 (i.e, the ridge regression) is studied. The case of p=1 corresponds to the lasso [11] and the general case of p ∈ [1,2] corresponds to the iterative shrinkage/thresholding algorithm (ISTA) of Daubechies, et al [5]. We will apply the proximal-gradient methods to prove convergence of our primal-dual fixed point methods for the general l_p-regularization, and also for the elastic net problem [14].

Key Words and Phrases: Prime-dual method, fixed point method, lasso, elastic net, regularization.

2010 Mathematics Subject Classification: 47H10, 47J25, 90C25, 90C46.

Published on-line: June 15th, 2023.

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