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Nonsingularity of FB system and constraint nondegeneracy in semidefinite programming

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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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Authors and Affiliations

  1. Department of Mathematics, South China University of Technology, Guangzhou, China

    Le Han, Shujun Bi & Shaohua Pan

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  1. Le Han
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  2. Shujun Bi
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  3. Shaohua Pan
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Correspondence to Le Han.

Additional information

This work is supported by National Young Natural Science Foundation (No. 10901058) and the Fundamental Research Funds for the Central Universities.

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Han, L., Bi, S. & Pan, S. Nonsingularity of FB system and constraint nondegeneracy in semidefinite programming. Numer Algor 62, 79–113 (2013). https://doi.org/10.1007/s11075-012-9567-9

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  • DOI: https://doi.org/10.1007/s11075-012-9567-9

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