Article ID: | iaor2013597 |
Volume: | 62 |
Issue: | 1 |
Start Page Number: | 79 |
End Page Number: | 113 |
Publication Date: | Jan 2013 |
Journal: | Numerical Algorithms |
Authors: | Pan Shaohua, Bi Shujun, Han Le |
Keywords: | programming (semidefinite), KuhnTucker conditions |
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.