High-Order Optimization Methods for Fully Composite Problems

Nikita Doikov () and Yurii Nesterov ()
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Nikita Doikov: Université catholique de Louvain, ICTEAM
Yurii Nesterov: Université catholique de Louvain, LIDAM/CORE, Belgium

No 3241, LIDAM Reprints CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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.

Keywords: Convex optimization; constrained optimization; nonsmooth optimization; gradient methods; high-order methods; accelerated algorithms (search for similar items in EconPapers)
Pages: 26
Date: 2023-01-01
Note: In: SIAM Journal on Optimization, 2022, vol. 32(3), p. 2402-2427
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvrp:3241

DOI: 10.1137/21M1410063

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