Lipschitz Stability of Least-Squares Problems Regularized by Functions with C2-Cone Reducible Conjugates

• 成果类型: Article; Early Access
• 署名作者: Cui, Ying; Hoheisel, Tim; Nghia, Tran T. A.; Sun, Defeng
• 署名单位: University of California System; University of California Berkeley; McGill University; Oakland University; Hong Kong Polytechnic University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2024.0692
• 发表日期: 2026-01-05
• 关键词: least-squares; Lipschitz stability; full stability; tilt stability; Convex Optimization; Lasso; variational analysis and nonsmooth optimization; second-order analysis; regularized problem

摘要

In this paper, we study Lipschitz continuity of the solution mappings of regularized least-squares problems for which the convex regularizers have (Fenchel) conjugates that are C2-cone reducible. Our approach, by using Robinson's strong regularity on the dual problem, allows us to obtain new characterizations of Lipschitz stability that rely solely on firstorder information, thus bypassing the need to explore second-order information (curvature) of the regularizer. We show that these solution mappings are automatically Lipschitz continuous around the points in question whenever they are locally single-valued. We leverage our findings to obtain new characterizations of full stability and tilt stability for a broader class of convex additive-composite problems.