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Recursive Construction of Optimal Self-Concordant Barriers for Homogeneous Cones

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  • O. Shevchenko

    (Western Michigan University)

Abstract

We give a recursive formula for optimal dual barrier functions on homogeneous cones. This is done in a way similar to the primal construction of Güler and Tunçel (Math. Program. 81(1):55–76, 1998) by means of the dual Siegel cone construction of Rothaus (Bull. Am. Math. Soc. 64:85–86, 1958). We use invariance of the primal barrier function with respect to a transitive subgroup of automorphisms and the properties of the duality mapping, which is a bijection between the primal and the dual cones. We give simple direct proofs of self-concordance of the primal optimal barrier and provide an alternative expression for the dual universal barrier function.

Suggested Citation

  • O. Shevchenko, 2009. "Recursive Construction of Optimal Self-Concordant Barriers for Homogeneous Cones," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 339-354, February.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:2:d:10.1007_s10957-008-9451-x
    DOI: 10.1007/s10957-008-9451-x
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    References listed on IDEAS

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    1. Cardoso, Domingos Moreira & Vieira, Luis Almeida, 2006. "On the optimal parameter of a self-concordant barrier over a symmetric cone," European Journal of Operational Research, Elsevier, vol. 169(3), pages 1148-1157, March.
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    Cited by:

    1. Da Tian, 2014. "An entire space polynomial-time algorithm for linear programming," Journal of Global Optimization, Springer, vol. 58(1), pages 109-135, January.

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