The volumetric barrier for convex quadratic constraints
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Let Open image in new window where Open image in new window and Open image in new windowi is an n×n positive semidefinite matrix. We prove that the volumetric and combined volumetric-logarithmic barriers for Open image in new window are Open image in new window and Open image in new window self-concordant, respectively. Our analysis uses the semidefinite programming (SDP) representation for the convex quadratic constraints defining Open image in new window, 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 Open image in new window.
KeywordsVolumetric barrier Convex quadratic constraints Semidefinite programming
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