2025/10/08 by Xudong Li, Li, Xudong, Meixia Lin +3
Computer Science · Mathematics · #FOS: Mathematics #Mathematical Analysis and Transform Methods #Matrix Theory and Algorithms #Numerical methods in inverse problems #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2510.06642
openalex publication_date 2025/10/08 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
In this work, we study the affine-constrained ℓ1 regularizers, which frequently arise in statistical and machine learning problems across a variety of applications, including microbiome compositional data analysis and sparse subspace clustering. With the aim of developing scalable second-order methods for solving optimization problems involving such regularizers, we analyze the associated proximal mapping and characterize its generalized differentiability, with a focus on its B-subdifferential. The revealed structured sparsity in the B-subdifferential enables us to design efficient algorithms within the proximal point framework. Extensive numerical experiments on real applications, including comparisons with state-of-the-art solvers, further demonstrate the superior performance of our approach. Our findings provide new insights into the sensitivity and stability properties of affine-constrained nonsmooth regularizers, and contribute to the development of fast second-order methods for a class of structured, constrained sparse learning problems.