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Central path and Riemannian distances

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  • NESTEROV, Yurii
  • NEMIROVSKI, Arkadi

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 .

Suggested Citation

  • NESTEROV, Yurii & NEMIROVSKI, Arkadi, 2003. "Central path and Riemannian distances," LIDAM Discussion Papers CORE 2003051, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2003051
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2003.html
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    References listed on IDEAS

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    1. NESTEROV , Yu. & TODD, Mike, 2002. "On the Riemannian geometry defined by self-concordant barriers and interior-point methods," LIDAM Reprints CORE 1595, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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