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Primal Subgradient Methods with Predefined Step Sizes

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  • Nesterov, Yurii

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

Abstract

In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on knowledge of the optimal value of the objective function, need corrections when they are applied to optimization problems with constraints. Their proper modifications allow a significant acceleration of these schemes when the objective function has favorable properties (smoothness, strong convexity). We show how the new methods can be used for solving optimization problems with functional constraints with a possibility to approximate the optimal Lagrange multipliers. One of our primal-dual methods works also for unbounded feasible set.

Suggested Citation

  • Nesterov, Yurii, 2024. "Primal Subgradient Methods with Predefined Step Sizes," LIDAM Reprints CORE 3314, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3314
    DOI: https://doi.org/10.1007/s10957-024-02456-9
    Note: In: Journal of Optimization Theory and Applications, 2024
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