Article ID: | iaor2004371 |
Country: | United States |
Volume: | 27 |
Issue: | 1 |
Start Page Number: | 150 |
End Page Number: | 169 |
Publication Date: | Feb 2002 |
Journal: | Mathematics of Operations Research |
Authors: | Sun Jie, Sun DeFeng |
Matrix-valued functions play an important role in the development of algorithms for semidefinite programming problems. This paper studies generalized differential properties of such functions related to nonsmooth-smoothing Newton methods. The first part of this paper discusses basic properties such as the generalized derivative, Rademacher's theorem, ℬ-derivative, directional derivative, and semismoothness. The second part shows that the matrix absolute-value function, the matrix semidefinite-projection function, and the matrix projective residual function are strongly semismooth.