A second-order method for strongly convex -regularization problems

• 成果类型: Article
• 署名作者: Fountoulakis, Kimon; Gondzio, Jacek
• 署名单位: University of Edinburgh; University of Edinburgh; Heriot Watt University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0875-4
• 发表日期: 2016
• 页码: 189-219
• 关键词: coordinate descent method; shrinkage

摘要

In this paper a robust second-order method is developed for the solution of strongly convex -regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently solved. The proposed approach is a primal-dual Newton conjugate gradients (pdNCG) method. Convergence properties of pdNCG are studied and worst-case iteration complexity is established. Numerical results are presented on synthetic sparse least-squares problems and real world machine learning problems.