Workshop Semidefinite Programming: Applications and Algorithms
ZIB-Berlin, November 15-17, 1998


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