On Some Works of Boris Teodorovich Polyak on the Convergence of Gradient Methods and Their Development
The paper presents a review of the current state of subgradient and accelerated convex optimization methods, including the cases with the presence of noise and access to various information about the objective function (function value, gradient, stochastic gradient, higher derivatives). For nonconvex problems, the Polyak–Lojasiewicz condition is considered and a review of the main results is given. The behavior of numerical methods in the presence of a sharp minimum is considered. The aim of this review is to show the influence of the works of B.T. Polyak (1935–2023) on gradient optimization methods and their surroundings on the modern development of numerical optimization methods.
Authors
- Darina Dvinskikh (ORCID: https://orcid.org/0000-0003-1757-1021)
- А. В. Гасников
- Fedor Stonyakin (ORCID: https://orcid.org/0000-0002-9250-4438)
- A. V. Lobanov (ORCID: https://orcid.org/0000-0003-1620-9581)
- Seydamet S. Ablaev (ORCID: https://orcid.org/0000-0002-9927-6503)
- Aleksandr Beznosikov (ORCID: https://orcid.org/0000-0002-3217-3614)
- S. M. Puchinin (ORCID: https://orcid.org/0009-0007-6918-6463)
Institutions
- Moscow Institute of Physics and Technology (RU)
- Institute for System Programming (RU)
- Institute for Information Transmission Problems (RU)
- V.I. Vernadsky Crimean Federal University (UA)
Publication Details
- Journal
- Журнал вычислительной математики и математической физики
- Published
- 2024-11-15
- DOI
- https://doi.org/10.31857/s0044466924040028
- Citations
- 1
- Primary Topic
- Numerical methods in inverse problems
- Type
- article
- Field-Weighted Citation Impact
- 0.89