Optimization Methods for Fully Composite Problems

Doikov, Nikita;Nesterov, Yurii
(2021) , 27 pages

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  • Doikov, NikitaUCLouvain
    Author
  • Nesterov, YuriiUCLouvain
    Author
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.
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Doikov, N., & Nesterov, Y. (2021). Optimization Methods for Fully Composite Problems (LIDAM Discussion Paper CORE 2021/01). https://hdl.handle.net/2078.5/166804