期刊
MATHEMATICS OF OPERATIONS RESEARCH
卷 27, 期 1, 页码 150-169出版社
INFORMS
DOI: 10.1287/moor.27.1.150.342
关键词
matrix functions; Newton's method; nonsmooth optimization; semidefinite programming
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.
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