Nonsingularity of FB system and constraint nondegeneracy in semidefinite programming

Nonsingularity of FB system and constraint nondegeneracy in semidefinite programming

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Article ID: iaor2013597
Volume: 62
Issue: 1
Start Page Number: 79
End Page Number: 113
Publication Date: Jan 2013
Journal: Numerical Algorithms
Authors: , ,
Keywords: programming (semidefinite), KuhnTucker conditions
Abstract:

For a KKT point of the linear semidefinite programming (SDP), we show that the nonsingularity of the B‐subdifferential of Fischer‐Burmeister (FB) nonsmooth system, the nonsingularity of Clarke’s Jacobian of this system, and the primal and dual constraint nondegeneracies, are all equivalent. Also, each of these conditions is equivalent to the nonsingularity of Clarke’s Jacobian of the smoothed counterpart of FB nonsmooth system, which particularly implies that the FB smoothing Newton method may attain the local quadratic convergence without strict complementarity assumption. We also report numerical results of the FB smoothing method for some benchmark problems.

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