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Gradient methods with memory

Author

Listed:
  • Nesterov, Yurii

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

  • Florea, Mihai

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

Abstract

In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is used in the form of a piece-wise linear model of the objective function, which provides us with much better prediction abilities as compared with the standard linear model. To the best of our knowledge, this approach was never really applied in Convex Minimization to differentiable functions in view of the high complexity of the corresponding auxiliary problems. However, we show that all necessary computations can be done very efficiently. Consequently, we get new optimization methods, which are better than the usual Gradient Methods both in the number of oracle calls and in the computational time. Our theoretical conclusions are confirmed by preliminary computational experiments.

Suggested Citation

  • Nesterov, Yurii & Florea, Mihai, 2023. "Gradient methods with memory," LIDAM Reprints CORE 3230, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3230
    DOI: https://doi.org/10.1080/10556788.2020.1858831
    Note: In: Optimization Methods and Software, 2022, vol. 37(3), p. 936-953
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