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Dual extrapolation and its applications for solving variational inequalities and related problems

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  • NESTEROV, Yu

Abstract

In this paper we suggest new dual methods for solving variational inequalities with monotone operators. We show that with an appropriate step-size strategy, our method is optimal both for Lipschitz continuous operators (O(1/e)iterations), and for the operators with bounded variations(0 (1/e2)). Our technique can be applied for solving non smooth convex minimization problems with known structure. In this case the worst-case complexity bound is 0(1/e)iterations.

Suggested Citation

  • NESTEROV, Yu, 2003. "Dual extrapolation and its applications for solving variational inequalities and related problems," LIDAM Discussion Papers CORE 2003068, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2003068
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    References listed on IDEAS

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    1. NESTEROV, Yurii, 2003. "Excessive gap technique in non-smooth convex minimization," LIDAM Discussion Papers CORE 2003035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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).
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    Cited by:

    1. NESTEROV, Yu., 2006. "Cubic regularization of Newton’s method for convex problems with constraints," LIDAM Discussion Papers CORE 2006039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Fedor Stonyakin & Alexander Gasnikov & Pavel Dvurechensky & Alexander Titov & Mohammad Alkousa, 2022. "Generalized Mirror Prox Algorithm for Monotone Variational Inequalities: Universality and Inexact Oracle," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 988-1013, September.
    3. NESTEROV, Yu., 2005. "Minimizing functions with bounded variation of subgradients," LIDAM Discussion Papers CORE 2005079, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. NESTEROV, Yu., 2005. "Primal-dual subgradient methods for convex problems," LIDAM Discussion Papers CORE 2005067, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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