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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. 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).
    3. 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.
    4. 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).

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