Nonsingularity conditions for the fischer-burmeister system of nonlinear SDPs

Shujun Bi, Shaohua Pan, Jein Shan Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


For a locally optimal solution to the nonlinear semidefinite programming problem, under Robinson's constraint qualification, we show that the nonsingularity of Clarke's Jacobian of the Fischer-Burmeister (FB) nonsmooth system is equivalent to the strong regularity of the Karush- Kuhn-Tucker point. Consequently, from Sun's paper [Math. Oper. Res., 31 (2006), pp. 761-776] the semismooth Newton method applied to the FB system may attain the locally quadratic convergence under the strong second order sufficient condition and constraint nondegeneracy.

Original languageEnglish
Pages (from-to)1392-1417
Number of pages26
JournalSIAM Journal on Optimization
Issue number4
Publication statusPublished - 2011


  • Clarke's Jacobian
  • Nonlinear semidefinite programming problem
  • Nonsingularity
  • Strong regularity
  • The FB system

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Applied Mathematics


Dive into the research topics of 'Nonsingularity conditions for the fischer-burmeister system of nonlinear SDPs'. Together they form a unique fingerprint.

Cite this