On a semi-smooth Newton method and its globalization

• 成果类型: Article
• 署名作者: Ito, Kazufumi; Kunisch, Karl
• 署名单位: University of Graz; North Carolina State University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-007-0196-3
• 发表日期: 2009
• 页码: 347-370
• 关键词: active set method; complementarity-problems; nonsmooth equations; optimization; semismooth; algorithms

摘要

This paper addresses the globalization of the semi-smooth Newton method for non-smooth equations F(x) = 0 in R-m with applications to complementarity and discretized l(1)-regularization problems. Assuming semi-smoothness it is shown that super-linearly convergent Newton methods can be globalized, if appropriate descent directions are used for the merit function |F(x)|(2). Special attention is paid to directions obtained from the primal-dual active set strategy.