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

作者：Yang Ching Yu; Chang Yu Lin; Chen Jein Shan^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(16): 5766-5783.

DOI：10.1016/j.na.2011.05.068

• Hilbert space
• Infinite-dimensional second-order cone
• Strong semismoothness

Given a Hilbert space H, the infinite-dimensional Lorentz/second-order cone K is introduced. For any x is an element of H, a spectral decomposition is introduced, and for any function f : R -> R, we define a corresponding vector-valued function f(H) (x) on Hilbert space H by applying f to the spectral values of the spectral decomposition of x is an element of H with respect to K. We show that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity, differentiability, smoothness, as well as s-semismoothness. These results can be helpful for designing and analyzing solution methods for solving infinite-dimensional second-order cone programs and complementarity problems.

• 出版日期2011-11