Newton-type multilevel optimization method. (2nd January 2022)

• Record Type: Journal Article
• Authors: Ho, Chin Pang; Kočvara, Michal; Parpas, Panos
• Is Part Of: Optimization methods and software. Volume 37:Number 1(2022)
• Page Start: 45
• Page End: 78
• Publication Date: 2022-01-02
• Subjects: Newton's method -- multilevel algorithms -- multigrid methods -- unconstrained optimization; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2019.1700256
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : 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.