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High-Order Optimization Methods for Fully Composite Problems

Author

Listed:
  • Doikov, Nikita

    (Université catholique de Louvain, ICTEAM)

  • Nesterov, Yurii

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

Abstract

In this paper, we study a fully composite formulation of convex optimization problems, which includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems with simple nondifferentiable components. We treat all these formulations in a unified way, highlighting the existence of very natural optimization schemes of different order p \geq 1. As the result, we obtain new high-order (p \geq 2) optimization methods for composite formulation. We prove the global convergence rates for them under the most general conditions. Assuming that the upper-level component of our objective function is subhomogeneous, we develop efficient modification of the basic fully composite first-order and second-order methods and propose their accelerated variants.

Suggested Citation

  • Doikov, Nikita & Nesterov, Yurii, 2023. "High-Order Optimization Methods for Fully Composite Problems," LIDAM Reprints CORE 3241, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3241
    DOI: https://doi.org/10.1137/21M1410063
    Note: In: SIAM Journal on Optimization, 2022, vol. 32(3), p. 2402-2427
    as

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