Optimization Methods for Fully Composite Problems

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

No 2021001, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite Minimization, where the objective can have simple nondifferential components. We treat all these formulations in a unified way, highlighting the existence of very natural optimization schemes of different order. We prove the global convergence rates for our methods 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: 27
Date: 2021-03-20
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2021001

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