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Towards nonsymmetric conic optimization




In this paper we propose a new interior-point method, which is based on an extension of the ideas of self-scaled optimization to the general cases. We suggest using the primal correction process to find a scaling point. This point is used to compute a strictly feasible primal-dual pair by simple projection. Then, we define an affine-scaling direction and perform a prediction step. This is the only moment when the dual barrier is used. Thus, we need only to compute its value, which can even be done approximately. In the second part of the paper we develop a 4n-self-concordant barrier for n-dimensional p-cone, which can be used for numerical testing of the proposed technique.

Suggested Citation

  • NESTEROV, Yu., 2006. "Towards nonsymmetric conic optimization," CORE Discussion Papers 2006028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2006028

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    References listed on IDEAS

    1. NESTEROV , Yurii & TODD , Michael, 1995. "Primal-Dual Interior-Point Methods for Self-Scaled Cones," CORE Discussion Papers 1995044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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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