Nonsingularity conditions for the fischer-burmeister system of nonlinear SDPs

Shujun Bi, Shaohua Pan, Jein-Shan Chen

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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
Volume21
Issue number4
DOIs
Publication statusPublished - 2011 Dec 1

Fingerprint

Nonsingularity
Nonlinear programming
Newton-Raphson method
Sun
Strong Regularity
Semismooth Newton Method
Second-order Sufficient Conditions
Quadratic Convergence
Constraint Qualifications
Nondegeneracy
Semidefinite Programming
Nonlinear Programming
Optimal Solution

Keywords

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

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science

Cite this

Nonsingularity conditions for the fischer-burmeister system of nonlinear SDPs. / Bi, Shujun; Pan, Shaohua; Chen, Jein-Shan.

In: SIAM Journal on Optimization, Vol. 21, No. 4, 01.12.2011, p. 1392-1417.

Research output: Contribution to journalArticle

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