0532968 20240103224520.420201012235959.9 85076357344 000502443800001 10.1080/10556788.2019.1700256 34 s. P cav_un_epca*02545881055-6788371 (2022)45-78Taylor & Francis Newton's method multilevel algorithms multigrid methods unconstrained optimization cav_un_auth*0396914 Ho Ch. P. GB 33 cav_un_auth*0101131 Kočvara Michal UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory 34 Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0396915 Parpas P. GB 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. WOS BA 10000 10100 10101 2023 3 RVO:67985556 http://hdl.handle.net/11104/0311787 S 3+4 Article Computer Science Software Engineering|Operations Research Management Science|Mathematics Applied C OPERATIONSRESEARCH&MANAGEMENTSCIENCE|COMPUTERSCIENCE.SOFTWAREENGINEERING|MATHEMATICS.APPLIED 2.1 0.4 10.7 0.00319 1.039 2342 1.079 2.200 49 Q1 57.4 Q1 Q2 0.69 Q2 81.8 2022 85076357344 SCOPUS PUBMED 000502443800001 WOS cav_un_epca*0254588 Optimization Methods & Software 1055-6788 1029-4937 Roč. 37 č. 1 2022 45 78 Taylor & Francis