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Rounding of convex sets and efficient gradient methods for linear programming problems

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  • NESTEROV, Yu

Abstract

In this paper we propose new efficient gradient schemes for two non-trivial classes of linear programming problems. These schemes are designed to compute approximate solutions withrelative accuracy . We prove that the upper complexity bound for both ln schemes is O( n m ln n) iterations of a gradient-type method, where n and m, (n

Suggested Citation

  • NESTEROV, Yu, 2004. "Rounding of convex sets and efficient gradient methods for linear programming problems," LIDAM Discussion Papers CORE 2004004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2004004
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2004.html
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    References listed on IDEAS

    as
    1. NESTEROV, Yu., 2003. "Smooth minimization of non-smooth functions," LIDAM Discussion Papers CORE 2003012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. NESTEROV, Yu, 2003. "Unconstrained convex minimization in relative scale," LIDAM Discussion Papers CORE 2003096, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Wei-jie Cong & Hong-wei Liu & Feng Ye & Shui-sheng Zhou, 2012. "Rank-two update algorithms for the minimum volume enclosing ellipsoid problem," Computational Optimization and Applications, Springer, vol. 51(1), pages 241-257, January.

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