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Gradient Methods for Stochastic Optimization in Relative Scale

Author

Listed:
  • Nesterov, Yurii

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

  • Rodomanov, Anton

    (ICTEAM)

Abstract

We propose a new concept of a relatively inexact stochastic subgradient and present novel first-order methods that can use such objects to approximately solve convex optimization problems in relative scale. An important example where relatively inexact subgradients naturally arise is given by the Power or Lanczos algorithms for computing an approximate leading eigenvector of a symmetric positive semidefinite matrix. Using these algorithms as subroutines in our methods, we get new optimization schemes that can provably solve certain large-scale Semidefinite Programming problems with relative accuracy guarantees by using only matrix-vector products.

Suggested Citation

  • Nesterov, Yurii & Rodomanov, Anton, 2024. "Gradient Methods for Stochastic Optimization in Relative Scale," LIDAM Discussion Papers CORE 2024027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2024027
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    References listed on IDEAS

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    1. Yurii Nesterov, 2018. "Lectures on Convex Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-91578-4, March.
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