Analysis of nonsmooth vector-valued functions associated with second-order cones

• 成果类型: Article; Proceedings Paper
• 署名作者: Chen, JS; Chen, X; Tseng, P
• 署名单位: University of Washington; University of Washington Seattle; Massachusetts Institute of Technology (MIT)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-004-0538-3
• 发表日期: 2004
• 页码: 95-117
• 关键词: Convergence analysis; newton methods; semidefinite; algorithms

摘要

Let K-n be the Lorentz/second-order cone in R-n. For any function f from R to R, one can define a corresponding function f(soc)(x) on R-n by applying f to the spectral values of the spectral decomposition of x is an element of R-n with respect to K-n. We show that this vector-valued function inherits from f the properties of continuity, (local) Lipschitz continuity, directional differentiability, Frechet differentiability, continuous differentiability, as well as (rho-order) semismoothness. These results are useful for designing and analyzing smoothing methods and nonsmooth methods for solving second-order cone programs and complementarity problems.