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


  • 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.

Suggested Citation

  • 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).
  • Handle: RePEc:cor:louvco:1994062

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    1. Tabellini, Guido, 2000. " A Positive Theory of Social Security," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(3), pages 523-545, June.
    2. Tabellini, Guido, 1991. "The Politics of Intergenerational Redistribution," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 335-357, April.
    3. Laurence J. Kotlikoff & Daniel E. Smith, 1983. "Introduction to "Pensions in the American Economy"," NBER Chapters,in: Pensions in the American Economy, pages 1-19 National Bureau of Economic Research, Inc.
    4. Kotlikoff, Laurence J. & Smith, Daniel E., 1984. "Pensions in the American Economy," National Bureau of Economic Research Books, University of Chicago Press, edition 0, number 9780226451466.
    5. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, January.
    6. Becker, Gary S & Murphy, Kevin M, 1988. "The Family and the State," Journal of Law and Economics, University of Chicago Press, vol. 31(1), pages 1-18, April.
    7. H. Verbon, 1987. "The rise and evolution of public pension systems," Public Choice, Springer, vol. 52(1), pages 75-100, January.
    8. Laurence J. Kotlikoff, 1987. "Justifying Public Provision of Social Security," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 6(4), pages 674-696.
    9. Samuelson, Paul A, 1975. "Optimum Social Security in a Life-Cycle Growth Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(3), pages 539-544, October.
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    Cited by:

    1. Ali Mohammad-Nezhad & Tamás Terlaky, 2017. "A polynomial primal-dual affine scaling algorithm for symmetric conic optimization," Computational Optimization and Applications, Springer, vol. 66(3), pages 577-600, April.
    2. 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.
    3. Maziar Salahi & Renata Sotirov & Tamás Terlaky, 2004. "On self-regular IPMs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(2), pages 209-275, December.
    4. Sturm, J.F., 2001. "Avoiding Numerical Cancellation in the Interior Point Method for Solving Semidefinite Programs," Discussion Paper 2001-27, Tilburg University, Center for Economic Research.
    5. Arjan B. Berkelaar & Jos F. Sturm & Shuzhong Zhang, 1997. "Polynomial Primal-Dual Cone Affine Scaling for Semidefinite Programming," Tinbergen Institute Discussion Papers 97-025/4, Tinbergen Institute.
    6. J.F. Sturm & S. Zhang, 1998. "On Sensitivity of Central Solutions in Semidefinite Programming," Tinbergen Institute Discussion Papers 98-040/4, Tinbergen Institute.
    7. 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.
    8. 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).
    9. Alemseged Weldeyesus & Mathias Stolpe, 2015. "A primal-dual interior point method for large-scale free material optimization," Computational Optimization and Applications, Springer, vol. 61(2), pages 409-435, June.
    10. NESTEROV, Yu., 2006. "Towards nonsymmetric conic optimization," CORE Discussion Papers 2006028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).


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