High-Order Optimization Methods for Fully Composite Problems
(2022) SIAM Journal on Optimization — Vol. 32, n° 3, p. 2402-2427 (2022)
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- Authors
Doikov, Nikita 
Nesterov, Yurii
- Abstract
- In this paper, we study a fully composite formulation of convex optimization prob-lems, which includes, as a particular case, the problems with functional constraints, max-type min-imization problems, and problems with simple nondifferentiable components. We treat all theseformulations in a unified way, highlighting the existence of very natural optimization schemes ofdifferent orderp\geq 1. As the result, we obtain new high-order (p\geq 2) optimization methods forcomposite formulation. We prove the global convergence rates for them under the most generalconditions. 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 methodsand propose their accelerated variants
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Citations
Doikov, N., & Nesterov, Y. (2022). High-Order Optimization Methods for Fully Composite Problems. SIAM Journal on Optimization, 32(3), 2402-2427. https://doi.org/10.1137/21m1410063 (Original work published 2022)