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https://scholarbank.nus.edu.sg/handle/10635/44209
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 | URI: | http://scholarbank.nus.edu.sg/handle/10635/44209 | ISSN: | 0364765X |
Appears in Collections: | Staff Publications |
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