Kurt Anstreicher
"The volumetric barrier for semidefinite programming"
We consider the volumetric barrier for the feasible region of a standard
form SDP. We use Kronecker product characterizations of the gradient and
Hessian of the volumetric barrier to obtain extensions of several
fundamental inequalities for the polyhedral volumetric barrier to the SDP
case. These extensions facilitate an improved self-concordancy analysis for
the semidefinite volumetric, and hybrid volumetric-logarithmic, barriers.
We also apply our results for the SDP case to obtain new self-concordancy
results for the volumetric barrier for convex quadratic constraints.
helmberg@zib.de
Last Update: October 1, 1998