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Constructing self-concordant barriers for convex cones


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    In this paper we develop a technique for constructing self-concordant barriers for convex cones. We start from a simple proof for a variant of standard result [1] on transformation of a -self-concordant barrier for a set into a self-concordant barrier for its conic hull with parameter (3.08 + 3.57)2 . Further, we develop a convenient composition theorem for constructing barriers directly for convex cones. In particular, we can construct now good barriers for several interesting cones obtained as a conic hull of epigraph of a univariate function. This technique works for power functions, entropy, logarithm and exponent function, etc. It provides a background for development of polynomial-time methods for separable optimization problems. Thus, our abilities in constructing good barriers for convex sets and cones become now identical.

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    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2006030.

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    Date of creation: 00 Mar 2006
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    Handle: RePEc:cor:louvco:2006030

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    Keywords: primal-dual conic optimization problem; self-concordant barriers; interior-point methods; barrier calculus;


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    1. NESTEROV ., Yurii E. & TODD , Michael J, 1994. "Self-Scaled Cones and Interior-Point Methods in Nonlinear Programming," CORE Discussion Papers 1994062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:
    1. NESTEROV, Yu., 2006. "Nonsymmetric potential-reduction methods for general cones," CORE Discussion Papers 2006034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).


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