Mathematical Programming

, Volume 100, Issue 3, pp 613-662

First online:

The volumetric barrier for convex quadratic constraints

  • Kurt M. AnstreicherAffiliated withDepartment of Management Sciences, University of Iowa Email author 

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Let where and i is an n×n positive semidefinite matrix. We prove that the volumetric and combined volumetric-logarithmic barriers for are and self-concordant, respectively. Our analysis uses the semidefinite programming (SDP) representation for the convex quadratic constraints defining , and our earlier results on the volumetric barrier for SDP. The self-concordance results actually hold for a class of SDP problems more general than those corresponding to the SDP representation of .


Volumetric barrier Convex quadratic constraints Semidefinite programming