Semismooth matrix-valued functions

Defeng Sun, J. Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

137 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)150-169
Number of pages20
JournalMathematics of Operations Research
Volume27
Issue number1
DOIs
Publication statusPublished - 1 Jan 2002
Externally publishedYes

Keywords

  • Matrix functions
  • Newton's method
  • Nonsmooth optimization
  • Semidefinite programming

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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