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


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    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

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    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2004004.

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    Date of creation: 00 Feb 2004
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    Handle: RePEc:cor:louvco:2004004

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    Keywords: nonlinear optimization; convex optimization; complexity bounds; relative accuracy; fully polynomial approximation schemes; gradient methods; optimal methods;


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    1. NESTEROV, Yu, 2003. "Unconstrained convex minimization in relative scale," CORE Discussion Papers 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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