The Volumetric Barrier for Semidefinite Programming
Kurt M. Anstreicher
We consider the volumetric barrier for semidefinite programming, or
"generalized" volumetric barrier, as introduced by Nesterov and Nemirovskii.
We extend several fundamental properties of the volumetric barrier for a
polyhedral set to the semidefinite case. Our analysis facilitates
a simplified proof of self-concordancy for the semidefinite volumetric
barrier, as well as for the combined volumetric-logarithmic barrier
for semidefinite programming. For both of these barriers we obtain
self-concordancy parameters equal to those previously shown to hold in the
polyhedral case.
Contact:
kurt-anstreicher@uiowa.edu
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