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Self-Scaled Cones and Interior-Point Methods in Nonlinear Programming


Author Info

  • NESTEROV ., Yurii E.

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • TODD , Michael J

    (School of Operations Research and Industrial Engineering, Cornell University)


This paper provides a theoretical foundation for efficient interior-point algorithms for nonlinear programming problems expressed in conic form, when the cone and its associated barrier are self-scaled. For such problems we devise long-step and symmetric primal-dual methods. Because of the special properties of these cones and barriers, our algorithms can take steps that go typically a large fraction of the way to the boundary of the feasible region, rather than being confined to a ball of unit radius in the local norm defined by the Hessian of the barrier.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1994062.

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Date of creation: 01 Nov 1994
Date of revision:
Handle: RePEc:cor:louvco:1994062

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Keywords: Nonlinear programming; conical form; interior point algorithms; selfconcordant barrier; self-scaled cone; self-scaled barrier; path-following algorithms; potential-reduction algorithms;


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Cited by:
  1. Sotirov, R. & Salahi , M. & Terlaky , T., 2004. "On Self-Regular IPMs," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3108007, Tilburg University.
  2. NESTEROV, Yu., 2006. "Towards nonsymmetric conic optimization," CORE Discussion Papers 2006028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Berkelaar, A.B. & Sturm, J.F. & Zhang, S., 1996. "Polynomial Primal-Dual Cone Affine Scaling for Semidefinite Programming," Econometric Institute Research Papers EI 9667-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  4. NESTEROV, Yu., 2006. "Constructing self-concordant barriers for convex cones," CORE Discussion Papers 2006030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Sturm, J.F., 2002. "Implementation of Interior Point Methods for Mixed Semidefinite and Second Order Cone Optimization Problems," Discussion Paper 2002-73, Tilburg University, Center for Economic Research.
  6. Klerk, E. de & Roos , C. & Terlaky, T., 1999. "Primal-dual potential reduction methods for semidefinite programming using affine-scaling directions," Open Access publications from Tilburg University urn:nbn:nl:ui:12-226131, Tilburg University.


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