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The volumetric barrier for convex quadratic constraints

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Abstract.

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 .

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Authors and Affiliations

  1. Department of Management Sciences, University of Iowa, Iowa City, IA 52242, USA

    Kurt M. Anstreicher

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  1. Kurt M. Anstreicher
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Correspondence to Kurt M. Anstreicher.

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Mathematics Subject Classification (1991):90C25, 90C30

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Anstreicher, K. The volumetric barrier for convex quadratic constraints. Math. Program., Ser. A 100, 613–662 (2004). https://doi.org/10.1007/s10107-003-0513-4

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  • DOI: https://doi.org/10.1007/s10107-003-0513-4

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