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Title: Semismooth matrix-valued functions
Authors: Sun, D. 
Sun, J. 
Keywords: Matrix functions
Newton's method
Nonsmooth optimization
Semidefinite programming
Issue Date: 2002
Citation: Sun, D.,Sun, J. (2002). Semismooth matrix-valued functions. Mathematics of Operations Research 27 (1) : 150-169. ScholarBank@NUS Repository.
Abstract: 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.
Source Title: Mathematics of Operations Research
ISSN: 0364765X
Appears in Collections:Staff Publications

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