Recursive Construction of Optimal Self-Concordant Barriers for Homogeneous Cones

O. Shevchenko ()
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O. Shevchenko: Western Michigan University

Journal of Optimization Theory and Applications, 2009, vol. 140, issue 2, No 10, 339-354

Abstract: 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.

Keywords: Optimal self-concordant barriers; Duality; Homogeneous cones; Siegel cones; Legendre-Fenchel transformation; Universal barriers (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10957-008-9451-x

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