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Subgradient ellipsoid method for nonsmooth convex problems

Author

Listed:
  • Rodomanov, Anton

    (Université catholique de Louvain, ICTEAM)

  • Nesterov, Yurii

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

Abstract

In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth con- vex minimization problems, convex-concave saddle-point problems and variational inequalities with monotone operator. Our algorithm can be seen as a combination of the standard Subgradient and Ellipsoid methods. However, in contrast to the latter one, the proposed method has a reasonable convergence rate even when the dimen- sionality of the problem is sufficiently large. For generating accuracy certificates in our algorithm, we propose an efficient technique, which ameliorates the previously known recipes (Nemirovski in Math Oper Res 35(1):52–78, 2010).

Suggested Citation

  • Rodomanov, Anton & Nesterov, Yurii, 2023. "Subgradient ellipsoid method for nonsmooth convex problems," LIDAM Reprints CORE 3236, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3236
    DOI: https://doi.org/10.1007/s10107-022-01833-4
    Note: In: Mathematical Programming, 2023, vol. 199, p. 305-341
    as

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