Central path and Riemannian distances

Yurii Nesterov and Arkadi Nemirovski

No 2003051, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this paper we study the Riemannian length of the primal central path computed with respect to the local metric defined by a self-concordant function. We show that despite to some examples, in many important situations the length of this path is quite close to the length of geodesic curves. We show that in the case when the Riemannian structure of a bounded convex set is introduced by a v-self-concordant barrier, the central path is sub-geodesic up to the factor v 1/4 .

Keywords: Riemannan geometry; convex optimization; structural optimization; interior-point methods; path-following methods; self-concordant functions; polynomial-time methods (search for similar items in EconPapers)
Date: 2003-07
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2003051

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