Nonsingularity conditions for FB system of nonlinear SDPs 1

Abstract

For a locally optimal solution to the nonlinear semidefinite programming,<lb>under Robinson’s constraint qualification, we show that the nonsingularity of Clarke’s<lb>Jacobian of the Fischer-Burmeister (FB) nonsmooth system is equivalent to the strong<lb>regularity of the Karush-Kuhn-Tucker point. Consequently, from Sun’s paper (Mathe-<lb>matics of Operations Research, vol. 31, pp. 761-776, 2006), the semismooth Newton<lb>method applied to the FB system may attain the locally quadratic convergence under<lb>the strong second order sufficient condition and constraint nondegeneracy.

Cite this paper

@inproceedings{Bi2011NonsingularityCF, title={Nonsingularity conditions for FB system of nonlinear SDPs 1}, author={Shujun Bi and Shaohua Pan and Jein-Shan Chen}, year={2011} }