Efficient Computation of the Non-convex Quasi-norm Ball Projection with Iterative Reweighted Approach

Qi An; Jiao Wang; Zequn Niu; Nana Zhang

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arXiv · 2412.19541

Efficient Computation of the Non-convex Quasi-norm Ball Projection with Iterative Reweighted Approach

Qi An·Jiao Wang·Zequn Niu·Nana Zhang

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Abstract

In this study, we focus on computing the projection onto the $\ell_p$ quasi-norm ball, which is challenging due to the non-convex and non-Lipschitz nature inherent in the $\ell_p$ quasi-norm with $0<p<1$. We propose a novel localized approximation method that yields a Lipschitz continuous concave surrogate function for the $\ell_p$ quasi-norm with improved approximation quality. Building on this approximation, we enhance the state-of-the-art iterative reweighted algorithm proposed by Yang et al. (J Mach Learn Res 23:1-31, 2022) by constructing tighter subproblems. This improved algorithm solves the $\ell_p$ quasinorm ball projection problem through a series of tractable projections onto the weighted $\ell_1$ norm balls. Convergence analyses and numerical studies demonstrate the global convergence and superior computational efficiency of the proposed method.

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BibTeX RIS

Qi An, Jiao Wang, Zequn Niu, Nana Zhang. 2024-12-27. Efficient Computation of the Non-convex Quasi-norm Ball Projection with Iterative Reweighted Approach. https://arxiv.org/abs/2412.19541

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