Newton-type multilevel optimization method

0532968 - ÚTIA 2023 RIV GB eng J - Článek v odborném periodiku
Ho, Ch. P. - Kočvara, Michal - Parpas, P.
Newton-type multilevel optimization method.
Optimization Methods & Software. Roč. 37, č. 1 (2022), s. 45-78. ISSN 1055-6788. E-ISSN 1029-4937
Institucionální podpora: RVO:67985556
Klíčová slova: Newton's method * multilevel algorithms * multigrid methods * unconstrained optimization
Obor OECD: Pure mathematics
Impakt faktor: 2.2, rok: 2022
Způsob publikování: Omezený přístup
http://library.utia.cas.cz/separaty/2020/MTR/kocvara-0532968.pdf https://www.tandfonline.com/doi/full/10.1080/10556788.2019.1700256

Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the optimization model, and as a result, they outperform single-level methods, especially for large-scale models. The impressive performance of multilevel optimization methods is an empirical observation, and no theoretical explanation has so far been proposed. In order to address this issue, we study the convergence properties of a multilevel method that is motivated by second-order methods. We take the first step toward establishing how the structure of an optimization problem is related to the convergence rate of multilevel algorithms.
Trvalý link: http://hdl.handle.net/11104/0311787