Nonsingularity conditions for the fischer-burmeister system of nonlinear SDPs

Shujun Bi; Shaohua Pan; Jein Shan Chen

doi:10.1137/110824577

Nonsingularity conditions for the fischer-burmeister system of nonlinear SDPs

Shujun Bi, Shaohua Pan, Jein Shan Chen^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 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 language	English
Pages (from-to)	1392-1417
Number of pages	26
Journal	SIAM Journal on Optimization
Volume	21
Issue number	4
DOIs	https://doi.org/10.1137/110824577
Publication status	Published - 2011

Keywords

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

ASJC Scopus subject areas

Software
Theoretical Computer Science
Applied Mathematics

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10.1137/110824577

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title = "Nonsingularity conditions for the fischer-burmeister system of nonlinear SDPs",

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.",

keywords = "Clarke's Jacobian, Nonlinear semidefinite programming problem, Nonsingularity, Strong regularity, The FB system",

author = "Shujun Bi and Shaohua Pan and Chen, {Jein Shan}",

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AU - Bi, Shujun

AU - Pan, Shaohua

AU - Chen, Jein Shan

PY - 2011

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N2 - 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.

AB - 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.

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KW - Nonlinear semidefinite programming problem

KW - Nonsingularity

KW - Strong regularity

KW - The FB system

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Nonsingularity conditions for the fischer-burmeister system of nonlinear SDPs

Abstract

Keywords

ASJC Scopus subject areas

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