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Towards nonsymmetric conic optimization

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  • NESTEROV, Yu.

Abstract

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," LIDAM Discussion Papers CORE 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

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    1. Osman Güler, 1997. "Hyperbolic Polynomials and Interior Point Methods for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 350-377, May.
    2. Yu. E. Nesterov & M. J. Todd, 1997. "Self-Scaled Barriers and Interior-Point Methods for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 1-42, February.
    3. NESTEROV , Yurii & TODD , Michael, 1995. "Primal-Dual Interior-Point Methods for Self-Scaled Cones," LIDAM Discussion Papers CORE 1995044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. NESTEROV ., Yurii E. & TODD , Michael J, 1994. "Self-Scaled Cones and Interior-Point Methods in Nonlinear Programming," LIDAM Discussion Papers CORE 1994062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Robert Chares & François Glineur, 2008. "An interior-point method for the single-facility location problem with mixed norms using a conic formulation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(3), pages 383-405, December.
    2. Brendan O’Donoghue & Eric Chu & Neal Parikh & Stephen Boyd, 2016. "Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1042-1068, June.
    3. NESTEROV, Yu., 2006. "Constructing self-concordant barriers for convex cones," LIDAM Discussion Papers CORE 2006030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Krokhmal, Pavlo A. & Soberanis, Policarpio, 2010. "Risk optimization with p-order conic constraints: A linear programming approach," European Journal of Operational Research, Elsevier, vol. 201(3), pages 653-671, March.
    5. NESTEROV, Yu., 2006. "Nonsymmetric potential-reduction methods for general cones," LIDAM Discussion Papers CORE 2006034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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